Translation:Does he have a dictionary? Yes, in the desk.
Would I be right in thinking that yn y ddesg would mean something like "in the drawer of the desk", while ar y ddesg would mean "on (the surface of) the desk"?
Oh! Well I was thinking 'in the desk' i.e. one of those desks with the lift up lid - those are the learning desks I know and love .... oh dear.