Translation:Her mouth is small and cute.
You people just do not understand when it should be translated and when it shouldn't. That's because you keep chatting at the back of the classroom instead of listening to prof. Duo!! When 很 links a noun and an adjective (as in 嘴巴很小), it works as a verb (usually translated by "to be"), not as an intensifier. Basically, if you can't remove 很 from a sentence, it means it is a verb and that it should therefore be translated by "to be": Her mouth is small. If you can remove 很 from a sentence, it means it is working as an intensifier and you can translate as such. E.g. 她（很）喜欢玩游戏 She likes playing games (very much / a lot).
That may be how Duolingo translates 很. What I learned in an online Chinese class, however, is that it really depends on whether or not that is emphasized. It is certainly helpful to have your input on how to make Duo happy though, since that it what gets you to the next stage of learning. Thanks for the feedback!
I'm super super annoyed with the translations, they've already used 又 with an example in previous sentences and then they do a super confusing sentence like this one?
"她的嘴巴又小又可爱" Should be the answer for that translation. The correct translation for the characters should be "Her mouth is very small, so cute!"
As far as I can tell, adjectives in Chinese usually require an adverb when used as predicates. For example, 我高兴 (I'm happy) sounds funny, so an adverb like 很 is usually required, as in 我很高兴 (I'm [very] happy). Other examples are 我不高兴 (I'm not happy) and 我非常高兴 (I'm very happy). As far as I can tell, when 很 is used in these cases, it's more or less to satisfy a grammatical requirement to make the sentence less awkward, and it takes on a very weak meaning. In other words, it doesn't necessarily mean 'very' when used in this case. I guess for that, one would use 非常 instead of 很.
That said, I still think it 'Her mouth is very small and very cute' should be accepted. Either that or provide an explanation when 很 is taught for the first time.
It makes sense in a basic lesson on body parts. Generally, 口 includes the inside, while 嘴巴 refers to the lips and tongue (i.e. the visible part). See this post: https://forum.duolingo.com/comment/26652252/%E5%8F%A3-vs-%E5%98%B4%E5%B7%B4