"Where is your house then?"
Translation:Càite a bheil an taigh agad ma-thà?
Càite a bheil do thaigh ma-thà? may or may not be accepted as it is not very good Gaelic - see https://duome.eu/tips/en/gd#Body-2. I don't know if they would accept it here but you cannot complain if they don't.
But they will not accept Càite a bheil do taigh ma-thà? And remember the misleading feature of Duolingo that if you make a mistake it does not give you the nearest correct answer to what you wrote, but sometimes a completely different - but correct - answer. So with your small mistake it may have 'corrected' it to the agam construction even if it would have accepted the do thaigh version.
I got a really good explanation from silmeth when I asked about this in the context of body parts so I'll copy his response below:
That’s the distinction between alienable and inalienable possession. It is introduced in the Body 2 skill and also greatly explained in two articles: Possessives and syllabic structure or Ar n-Athair a tha air nèamh and Aig, air agus ann an or The severed head on the Akerbeltz wiki. In short – Gaelic expresses two kind of possession: * inalienable – things that are inherently yours and you cannot easily dispose of them or make them someone else’s: your body parts, family members, feelings… * alienable – things that you can buy or sell, pass along, mostly material possession but also more distant acquaintance with people… Inalienable possession is expressed by possessive pronouns, eg. my father is m’ athair, my hand is mo làmh, but alienable uses a different construction: an taigh agam my house. Of course there are exceptions (eg. my husband is an duine agam even though my wife is mo bhean), so you need to bear that in mind when you see one of those construction when you’d expect the other from the general pattern. You can read the tips and notes in the web browser version of Duolingo at https://duolingo.com and also on the https://duome.eu/tips/en/gd website. Unfortunately they are not available in the Duolingo mobile app. So you might want to open your web browser for reading. ---- As for your examples, it would be only an toil leat an deasg agam? because the desk is just your possession and not something inalienable. But if you really wanted to use the possessive pronoun for some reason (maybe to emphasize your connection to the desk in a poem or sth?) you would need lenition after mo, so mo dheasg (but generally you’d use an … agam here).
See my answer to a similar question. Both càite a bheil and càit a bheil mean the same, the former is an older spelling, the latter is a newer one with a silent vowel dropped, I think both should be accepted.
The lesson notes explain it as:
Càite a bheil?
The Gaelic Orthographic Conventions document (not a page turner) recommends this now be written as Càit a bheil. This is pronounced the same and both spellings are frequently seen, although the one we have used is more retro. We will probably update this in the next iteration of the course.