"I want the farmer's potatoes."
Translation:Dw i eisiau tatws y ffermwr.
Bit of a curveball here. Is this the standard way of assigning possession in Welsh?
This is explained with more examples in the notes for the later unit on 'Possession'.
In the noun–noun construction in Welsh, the first one is definite ("the") just because of the construction; it doesn't need (and can't take) an extra "the".
(Doing so would be like saying "the my book". Good Italian but but English—possessed things are definite by construction in English.)
So tatws ffermwr would be "the potatoes of a farmer" / "a farmer's potatoes" and *tatws y ffermwr" are "the potatoes of the farmer" / "the farmer's potatoes".
You can't put a "the" in front of that and say "the a farmer's potatoes" or "the the farmer's potatoes".