Several users have answered a similar question before, although I think that you should look into the follow up of the answers to have a more precise answer.

I'd like to add that it wasn't just in the middle ages, according to first hand stories of my parents, farm labourers in rural italy in the 60-70s would drink several liters of wine per day as a source of cheap energy (the quality of local wine was terrible). So I guess it comes down to getting used to it.

In addition to what has already been written, I am pretty sure that the data mentioned are either blatantly wrong, as it is physically very difficult and outright unsafe for an average person to drink 16 liters of any liquid in 24 hours. Thus, I;m pretty much that the information was either a result of mistake or a clear lack of understanding of nutrition basics by people at Hammershus.

It is possible that the authors of the information simply calculated the amount of beer that an average person would have drunk to satisfy their daily caloric requirement. This, of course is pretty much nothing more than a mental exercise, a people did not limit their diet to just beer (it is technically possible, although not a long-term solution). Average modern light beer (I'm using a 500 ml bottle as a reference) has roughly 250 kcal, what would more or less correspond to the beer in previous centuries, as the alcohol does not contribute its full energy due to relatively poor ability of human body to extract it. The amount of 6 litres of beer mentioned originally translates to 3000 kcal, what is quite the recommended daily caloric intake of a person performing physical work (and most people living in Middle Ages would have fallen into that category). Even if the beer was more caloric due to higher amount of unfermented carbohydrates, it would still be in the ballpark of normal energy intake for an average peasant of craftsman. So my bet is that the amount of 6 litres of beer was to mean a theoretical amount one should drink on a beer-only diet.

In addition, as already written by u/Daztur, medieval or generally pre-19th century beer was much weaker than modern one, as it was essentially made as an everyday drink. Although the only thing we have is a conjecture, it is not a mistake to assume that the average beer made at home was similar to a modern table beer or even weaker and thus contained 1-2% of alcohol. That's, on average 2-3 times less than an average European light beer (typically 4.5-5.5% ABV), thus drinking 2 litres of beer to quench thirst during the day would have amounted to the consumption of alcohol equivalent to a single 500 ml bottle or a pint of modern beer, while at the same time providing 1/3rd of the daily caloric intake with probiotics in the form of yeast remains, and substantial amount of B vitamins (niacine, riboflavine, pyridoxine) and micronutrients, chiefly magnesium and potassium.

By the same token, the claim about 16 litres of beer is quite hard to believe, as 8000 kcal is tremendous amount of energy, that is generally consumed only by people who exert their bodies to the peak of the human ability, such as Olympic class swimmers. Any person that simply works at their own pace, even doing energy-consuming tasks, like tree-felling or plowing would quickly get morbidly fat should they were consistently providing such amount of energy.

Well if you've known some functional alcoholics, they can go through a ludicrous amount of alcohol in a day by drinking small amounts of alcohol throughout the day and operating in a state of unending low-level drunkenness. Not a particularly good idea, but it's possible.

The other side of the coin is that a "liter" of beer isn't a measure of alcohol. A liter of small ale and a liter of barley wine are completely different things that have ENORMOUSLY different levels of alcohol. So how much alcohol was in a liter of beer? Well it depends on place and time and it's very difficult for us to reconstruct exactly. Part of the problem is that hydrometers (a very simple piece of technology, it's a little bob that you float in a liquid to measure how dense it is) weren't used at all in brewing until 1770 and took a while to catch on after that. Before the use of hydrometers, people didn't have a good way of measuring how much maltose (malt sugar) was in the beer before fermentation or how much of that maltose was converted into alcohol during fermentation.

The other half of the problem is that professional historians tend to write a lot about the socio-economic aspects of brewing and very little about the technical aspects of brewing or things like "how did the beer taste?" This means that if you DO care about things like "how specifically did the make the beer" or "how strong was it?" you have to rely mostly on amateur researchers, which raises a different set of issues.

So before the 19th century we're grasping around in the dark with regard to beer strength, but there are some reasons to think that at least some beer might've been quite weak back then. For example:

-Malting efficiency: malting is basically letting grains sprout a little bit, after which you generally roast the malted grain as it'll start rotting quite quickly otherwise. Malting techniques in the past (for example floor malting where you dump a bunch of grain on the floor and continually manually turn it over with shovels) were less efficient than modern methods and a lot of this malt was then cooked relatively dark. For a variety of chemical reasons, darker grain is more difficult to get maltose (malt sugar) out of than lighter grain, but people often preferred darker malt and it was generally cheaper than lighter malt ("white malt"). One reason that malting efficiency was low is that without hydrometers they didn't have any good way to check how efficient their methods were except tasting some wort (unfermented beer) and seeing how sweet it was.

-Mashing efficiency: mashing is basically stewing malt in warm water, which makes enzymes turn grain starches into maltose. You generally want to hit around 67 °C and, while there's some room for error, bad things can happen if you don't hit the right temperature and then maintain it for around an hour. This is obviously hard to do without a thermometer and people didn't use brewing thermometers until the mid 18th century and they took a while to catch on. Also, especially if you want to wring every last bit of efficiency out of the grain (or are using poorly modified malt), just holding the mash at 67 °C isn't your best bet. The most efficient way of going about things is a complicated process called "step mashing" where you heat up the mash a bit, let it sit at that temp for a while, hit it up a bit more to another very specific temperature, let it sit there for a while, etc. etc. for various chemical reasons. Again, not a fun thing to do without a thermometer. Also not fun if you don't have a proper brew pot and are heating the mash by throwing hot rocks into a bucket as happened in some cases. Also, again the biggest stumbling block is that if you want to experiment with a more efficient method of mashing there's no way to check if what you're doing is working (except "does this taste sweet?") without a hydrometer so if you look at medieval brewing texts you get some very backwards methods of mashing, including putting in very hot water first (to "open up the grain"), draining that off and putting in cooler water, which is exactly the opposite of what you want to be doing heat-wise. A lot of early mashing techniques also used a lot of water which further watered down the wort (unfermented beer) unless you spent a LONG time boiling it down which would be expensive due to fuel costs.

-Attenuation: OK, now you boil in some hops (if you're even using hops, which wasn't a given) and after you've malted your grain and mashed it and you've got a pot of sweet liquid (wort) that has to be fermented into beer. Yeast goes in somehow (including floating in from the air in some cases) and it eats the maltose in the wort and turns that into alcohol. The measurement of what percentage of the carbohydrates in the wort are turned into alcohol is called attenuation. About 75-80% is normal among modern ale homebrewers who know what they're doing (although some beers can get a good bit higher or lower) while large industrial breweries often get above 90% and the attenuation of lite beer/malt liquor can get ridiculously high. We don't know what kind of attenuation brewers were getting far in the past (again, no hydrometers so no way of measuring) but once we get reliable brewing records that measure this sort of thing in the 19th century some breweries posted very very low attenuation numbers. This was especially prevalent in northern German breweries brewing traditional beers such as Berliner Weisse, where I've seen a lot of attenuation numbers on the order of 50%. This means a whole lot of potential alcohol was just left on the table. A lot of these beers also had very low ABV compared to modern beer, some of them being around 2.5% ABV.

-Small ale: while some beer was made thumpingly strong and kept for months (high ABV helps with preservation), and the first British breweries to operate on an industrial scale in the 19th century put out a lot of strong beer, a lot of cheap beer was made quickly and drunk fresh (drinking beer very fresh gives any bacteria present less time to infect the beer) which, again, doesn't do any favors for efficiency. This very very fresh beer would've been sweet and very very caloric compared to his alcohol content which would've made it a good source of easily digestible calories for people doing hard labor. Also for poor people a lot of malt was reused. Either simply running water through old malt or mixing old malt and a bit of fresh malt to try to squeeze out a bit more maltose. This would result in very weak beer that you could drink an enormous amount of without getting drunk. How prevalent this kind of low alcohol beer was and just how low in alcohol it was (1% vs. 2.5% vs. 4% matters a lot if you're drinking it by the gallon) would vary a lot so again this is hard to nail down exactly until we start getting proper brewing records in the 19th century but a lot of people were drinking quite weak beer.