I am an Italian native speaker, and 'la' in this sentence might refer to a female subject "I cannot understand her", or it could be used in the polite form "I cannot understand you".
I'm trying to remember the polite form: if la was referring to polite you, would not the L be capitalized? Non La posso capire.
well, yes in principle it is more correct but both forms are now rather current. One would perhaps better say "non La capisco" in this case. I revised my previous comment.
Good to know for existence outside Duo - but if you try the formal you in Duo, unless it's written with a capital "L", or Duo pulls one of it's surprise grammar-tricks on us, "la" always means "her/it".
Given what you know about the real world, that's unfortunate, a bit.
'Comprehend' should be accepted. I concede that it's less usual in everyday English, but it's given in the choices so should be ok.
Even it can refer to a question (una domanda) and in this case it would be I cannot understand it. I think
How would you say "I don't understand her"? Would it be the same or different?
It is: "non la capisco", either if you are talking with someone about a woman, or in a one-to-one conversation if you want to use a formal expression. I revised my first comment
Hello! "non le posso capire" = I cannot understand them (where them is feminine plural)
In addition to being the direct object form of loro (le = "them"), le is also the indirect object form of lei, which may be what your confused about. As such, le means "to her/it, of her/it", and you don't understand "of" something or someone.
Rather, one understands direct objects, so la is required as it is the direct object form of lei.
"Her" or "it" is who or what you don't understand. In a parallel sentence:
Non posso capire la donna. Non la posso capire.
"I cannot understand the woman. I cannot understand her." [No hidden message here - I was just using the first feminine word that came to mind, to be consistent with the exercise.]
You can also say, Non posso capirla = "I cannot understand her."
I keep getting tripped up by the three "o" sounds in non la posso, which convinces me the I actually heard non lo posso instead of non la posso. The mind is a strange thing sometimes.