"He is your your changing?"
Anyone care to explain the logic behind this one? Haha
So? The hint is correct - look up do in the dictionary, and one of the definitions is indeed that do is a possessive adjective - "your". It's the first definition in the de facto standard dictionary Foclóir Gaeilge-Béarla
It's also the first definition in Duolingo's own dictionary:
There's nothing wrong with the hint - the hints aren't supposed to be a shortcut to the right answer, they're just a quick dictionary lookup, and they aren't tailored to each exercise. If you want to see the correct answer, just click "Submit".
Maybe it makes more sense if you go back a step first. I think you understand how this one works: Tá sé ag athrú an leabhair (literally He is at the changing of the book).
Now, when you want to use a pronoun (that is, to say me, you, him/her/it, us, you or them) instead of "an leabhair", you don't say the changing of you, but your changing. Which should probably make sense to you; at least to me "your" generally sounds more reasonable than "of you" even when looking at it in English.
Finally we get do instead of ag. This isn't how the logic of the language once worked, but at least in some dialects both were pronounced similar enough when combined with the pronouns that the original ag was eventually mistaken for do, and that's what the standard has today. Just remember that this happens with all pronouns before the verb.
So in the end we have: Tá sé do bhur n-athrú (He is at/to your changing).