Translation:They are going to spend their vacation in Eastern Europe.
In the U.S., Duo's "Eastern Europe" is quite commonly referred to as "East Europe". About 3 examples back, Duo translated "Asie de l'est" as "East Asia." This makes it appear to me that "East Europe" is a correct and acceptable translation, at least in the U.S. The inconsistency between "East Asia" and "Eastern Europe" for the exact same French is a bit jarring.
Usually, Asia is kind of split in 3 parts:
- L'Asie Mineure
- L'Asie Centrale
- L'Asie du Sud-Est or l'Extrême Orient.
"L'Asie de l'Est" is not something we use much, nor "'l'Asie orientale".
When it comes to "East(ern) Europe", we use "l'Europe de l'Est" and "l'Europe Centrale" which have tended to cover the same countries since the fall of the USSR.
I admit that my hearing is a skosh this side of deaf, but I defy anyone to distinguish this speaker's "leurs" from "la". In fact, I have noticed that in the last 2 or 3 weeks, BOTH speakers are shortening a number of 2-letter words ("ce" is another notorious example) to the point that it is often uncertain that ANYTHING was said, let alone being able to discern what.
I just listened to both voices. I can hear "leurs" all right but I am French.
Yet I also heard that they pronounce "est" (East) like "est" (is), which is wrong: in "de l'est", both the S and the T should be heard.
Back to "leurs" vs "la": even if you don't hear a difference, you might use your knowledge that "vacances" is always in the plural in French, so "la" is impossible.