Have you read this page?
It's all explained here: https://www.duolingo.com/skill/ga/Possessives/tips-and-notes
Long story short, instead of having a separate word for "his", "her", or "their" the way we do in English, Irish just has "a" and it's the next word that changes to indicate which it is.
Yeah, it can be confusing at first because the system is so different from what we're used to.
Whether "a" means "his", "her", or "their" depends on what happens to the start of the next word.
You would have given useful feedback to the administrators if you had clicked on the flag and typed in what you wrote above (maybe you did!).
I'm doing Duolingo Polish and it's really shocking how many wrong answers get through. I always check now on the comments page and send a flag message where required, if I'm in a good mood ;-)