It is slightly disturbing that a test should have offered a definitive 'correct' answer to that question. There is no definitive answer. There are however a number of attested events and trends that may provide clues as to what was happening in the Aegean in the Late Bronze Age.

First though, some terminology clarification. The Mycenaean civilisation was centred around a number of 'palaces', large heavily fortified structures that functioned as a combination of royal residence, military stronghold, resource storage and exchange and centre, and religious centre. The most famous of these was Mycenae, after which archaeologists named the civilisation. Broadly speaking the Mycenaean civilisation was on the Greek mainland, particularly the Argolid, Boiotia, Lakonia, but also in the west and north. They emerged from the 16th century, and really expanded in the 14th century BC.

The Minoans on the other hand were on Crete, and flourished a little earlier. After the 15th century BC, when many of the palaces in Crete suffered destruction, power became centralised at Knossos, and in the 14th and 13th centuries BC it seems that Mycenaeans were in power there.

So for the Minoans you could say that their fall came about because of Mycenaean invasion. As such, think of Crete at the end of the Bronze Age as Mycenaean. (This is very over simplistic in ways that I can expand on if you like, but it's not a bad way of holding a frame of reference).

So what we are really talking about is the fall of the Mycenaeans. Again, a clarification: this didn't happen overnight. We sometimes talk about the 'Collapse of 1200BC' but this is for convenience. Destructions and population movements were taking place from the mid 13th century, and continued, notwithstanding a brief resurgence in the mid 12th century, through to around 1100 BC.

So what was causing the destruction of the Mycenaean palaces? Let's start with straightforward ones. At Mycenae around 1200BC we know there was a big earthquake and much of the citadel was burned by the ensuing fire started in the damage. We know it was an earthquake because we have skeletons of people found crushed under fallen walls and buildings in the same way that happens in earthquakes today. We also have evidence of some buildings rebuilt with anti-seismic buttresses. But earthquakes are not that rare in the Aegean. Why had previous earthquakes not destroyed civilisations?

Another attempt of explanation would be invasion. Specifically this is attempted by bringing in the Dorian invasion. The Dorian invasion was an attempt to explain linguistic variations in Greeks 500-600 years later, and there is no archaeological evidence for the sweeping invasion and displacement by Dorians. No serious archaeologist of prehistoric Greece gives any support to a "Dorian invasion" hypothesis. This is not to say that warfare was not a problem. At some destruction sites we do not have the tell tale signs of earthquakes and invasion may seem more likely. It is sometimes suggested that the way in which Mycenaean palaces were heavily and increasingly fortified in the 14th and 13th centuries reflects an 'age of anxiety' and that the rulers felt fearful and felt the need to protect themselves. By extension we may deduce that warfare was a real concern and may have led to some of the destructions. In Crete there was a broad (but not universal) trend of people leaving coastal settlements and fleeing to the highlands, and settling in places that you really wouldn't live unless you were frightened to be near the sea (I have climbed these mountains...). As such some interpret this as signs that the sea peoples were marauding the Aegean in addition to bothering Egypt. This is totally feasible.

It has been pointed out by some archaeologists and historians that none of the war tactics or weapons we know from the Late Bronze Age could realistically have breached the immense defences and natural fortification of sites like Mycenae and Tiryns, and therefore posit that internal strife may be a more realistic option.

True enough, if there was ever a society where the 1% had it all, the kings of the Mycenaean palaces were them. The overwhelming centralisation of resources, wealth, trade, and power can lead to what Tainter calls a "dinosaur" model, that is, top heavy and incapable of swift change. Perhaps popular unrest bubbled over at the palaces.

There are more options: a volcanic eruption in Iceland (Hekla) is known to have affected the climate of the eastern Mediterranean (and elsewhere of course) in the 12th century, in a way comparable to the 19th century AD 'year without a summer'. Did famine cause civil unrest? Sue Sherratt suggests that Cypriot trade routes changed in the 13th century, cutting off some of the palaces and their kings. Did the loss of this revenue and the associated power of wealth cause a downfall of the system?

I have tried to pick out a selection of the more credible theories, but there are more out there, some getting a little bit wacky, so I stopped it there. But how to make sense of all these theories?

Increasingly popular in prehistoric and early Greek archaeology is a kind of all encompassing theory. Sue Sherratt calls it systems collapse, while Eric Cline talks about a 'perfect storm'. Basically, what these theories posit is that there was no single identifiable cause for the Mycenaean collapse. Earthquakes, famines, wars, and presumably internal strife and trade difficulties had all at some point afflicted the Mycenaeans in their preceding hundreds of years. What was unique in the final collapse was the inability to recover from them, and this can arguably only be explained by a concurrence of difficulties. For example, Mycenae experiences an earthquake and much of the palace is destroyed. The local elites look to recover the situation. The granary has gone, have we got more supplies? No we had crop failures. Ok we have a shipment arriving yeah? The sea peoples/pirates seized the ship. Ok we can send off for more by trade can't we? No the trade ships from Cyprus have stopped coming this way. Ok well get the people to rebid the walls for now. They're hungry and won't work. Get the guards. You have no food and nothing trade, how are you going to pay them? Cue a powerless King, a disgruntled population either leaving or fighting, and a society falling apart.

Tl;dr Complex societies are rarely brought down by one thing, but by many things happening at the same time