The Welsh sentence is missing the definite article (the) for potatoes:
"Dw i eisiau tatws y ffermwr." -- "I want the farmer's potatoes." --> Here, 'y ffermwr' translates to 'the farmer' and 'tatws' to 'potatoes'. With your sentence structure, it would look like so: "I want potatoes of the farmer."
"Dw i eisiau'r tatws y ffermwr." -- I want the potatoes of the farmer." --> Here, 'y ffermwr' translates to as 'the farmer' and ' 'r tatws' to 'the potatoes'.
Since the question asks for tatws, not 'r tatws, the definite article is wrong and marks the answer as incorrect.
I realize it's an old question, but I wondered for a moment as well, until I realized that, without the def. article, the translation into English would be really weird.
We explain this in the course notes - see the sticky discussion on course hints and tips at https://www.duolingo.com/topic/924/hot
In brief, the Welsh pattern x yr y translates as 'the y of the x*, with English adding an 'of' and an extra 'the'. Very often, though, the resulting English is awkward or wrong and a better translation is 'the x's y':
- tatws y ffermwr - (the potatoes of the farmer) = the farmer's potatoes
- car y dyn - (the car of the man) = the man's car
- gwaith yr adeiladwyr - (the work of the builders) = the builders' work
With proper nouns we do not need the 'r/yr/y in Welsh unless it is part of the proper noun, as it is with a few names of towns and countries or with some organisations. Sometimes the equivalent English form can use the proper noun or a related adjective to describe the thing 'owned'.
- car Dewi - (the car of Dewi) - Dewi's car
- llyfrgell Aber - (the library of Aber) - Aber's library, the Aber library
- senedd yr Alban - (the parliament of Scotland) - Scotland's parliament, the Scottish parliament