Translation:One woman cooks the fish, the other cooks the duck.
I used a semicolon instead of a comma, which I would think is correct. It certainly is correct in English. Maybe not in Italian?
Semicolon is not frequently used in Italian (even if it should be), indeed the sentence is good either with comma or semicolon
This translates to a run on sentence in English. I would break it into two sentences or say "and the other", but that was marked wrong.
"One woman cooks fish, the other duck" is also perfectly appropriate and acceptable English that means exactly the same thing as the Italian. The verb does not have to be repeated in such a construction (at least not in English).