They got in a fight deciding who's going to do what.
They had an argument about who will do what.
「ケンカする」は英語で get in a fight / have a fight / to fight / to argue / to have an argument などの言い方があります。
「誰が何をする」は英語で who is going to do what / who will do what と言います。
They got in a fight deciding who's going to do what / They had an argument about who will do what =「 誰が何をするかでケンカになった」となります。
どうぞご参考に。