This should be covered in the "Tips and Notes" for possessives: https://www.duolingo.com/skill/nb/Possessives
It depends on who "owns" the girl. If it's the subject's it is "si", if it's the object's it is "hans".
"Han liker jenta si." = "He likes his (own) girl."
"Han liker jenta hans." = "He likes his girl." (another person's girl)
I've never seen any of these helpful notes either for any of the languages I've done in a little over a year on Duolingo using my Android app. They didn't come up in the mobile view when trying to view the lesson on my Chrome browser either, BUT they 'magically' appeared after I touched the three dot menu in the upper right corner just now and selected: Request desktop site!!! So, this may work for you and many others too, when a little general explanation could help.
Understand the difference in subject and object here. fveldig said that if the subject owns the girl, then it's "si", but if it's the object that owns the girl, then it's "hans".
Subject means that the thing owning the girl has already been mentioned. So, in other words, "Jenta si" makes no grammatical sense. This could be "his girl" or "her girl" as there is no subject mentioned before.
Object means that there is a new thing owning the girl, or rather, that it is a newly mentioned object that does own the girl. That's why "Jenta hans" makes grammatical sense; even though there is no "han" at the beginning of the sentence, there doesn't have to be, because the object is being mentioned that own the girl, whereas before, no object was being mentioned.
Hopefully this makes sense. :)