This question comes up very often in my language classes, as this particular construction more closely resembles the way you would indicate possession in Dutch. Many of my students use 'the X of Y' rather than 'the Y's X' to indicate possession (meaning they would answer "the car of my dad" instead of "my dad's car" when prompted to indicate possession in some way) because in Dutch you would say "de auto van mijn vader" (which turns into "the car of my dad" when literally translated).
The problem is that my students have (rightfully) remarked that there are times where you would use that construction to indicate possession of some kind, but both my colleagues and I can't come to a conclusive answer as to when you would do that. This particular issue has been haunting my classes for the entire school year, and I would like to be able to offer a conclusive answer to my students the next time this comes up.
Thanks in advance!