In future queries, I suggest you give a descriptive title and an explanation in the body. Please also note that the purported date violates the 20-year rule of this subreddit (though the original story, from 1931 or 1987, doesn't).

This purports to be a radio conversation between a British aircraft carrier, "HMS Britannia", and what is eventually stated to be an Irish lighthouse.

There has never been a British aircraft carrier named HMS Britannia.

Very few lighthouses are staffed in the West in modern times -- they are automated. So it is highly improbable that a lighthouse would respond by radio.

The image says it was released by "Chief of Naval Operations". That is the officer serving as the service head of the United States Navy, on the US Joint Chiefs of Staff. It is not stated why a US naval officer would want to humiliate a close ally.

When you get forwarded jokes and stories, I suggest that people check Snopes: it's well-sourced and usually quite reliable. (The Straight Dope Web site has a larger variety of stories, but not quite as solid in some cases.) This is a classic urban legend, documented inter alia at Snopes, titled there Military: The Obstinate Lighthouse. The earliest instance they have is from 1931, but in the form of a joke. This image is based on the modern version, which I started seeing in the 1990s with US ships (and saw the Snopes debunking even then). They date this version to the Naval Institute Proceedings in 1987.