The Possessives and syllabic structure or Ar n-Athair a tha air nèamh article on the Akerbeltz wiki explains it nicely. It is also briefly described in the Body 2 skill’s Tips and notes.
It’s a difference between alienable and inalienable possession, things that are part of your body or your blood relatives are more likely to use the possessive pronouns (mo, do, ur, etc.) and things you can buy or sell basically always use an … agam, etc., but there are some exceptions.
The contributors would need to answer you to say what’s exactly their policy regarding what’s considered an acceptable answer.
But I would guess not, as more literally do you like the desk I have would be an toil leat an deasg a tha agam in Gaelic.
an deasg agam really just means my desk, you can think about it as the desk I have, but there is no verb in Gaelic here; English the desk of mine would be closer (and that too possibly could count as an acceptable answer). But the straightforward idiomatic English translation of Gaelic an X agam is just my X.
(Of course, in a real translation of a longer text, in context the X I have, or the X of mine, etc. might be better translations – just not necessarily in the course that teaches you the default most direct idiomatic translations.)