YOU SAID:
I don't like how you ate my cheese
INTO JAPANESE
私はあなたが私のチーズを食べたのが好きではありません
BACK INTO ENGLISH
I do not like that you ate my cheese
INTO JAPANESE
私はあなたが私のチーズを食べたことが気に入らない
BACK INTO ENGLISH
I do not like your eating my cheese
INTO JAPANESE
私はあなたのチーズを食べるのが嫌いです
BACK INTO ENGLISH
I do not like to eat your cheese
INTO JAPANESE
私はあなたのチーズを食べるのが好きではない
BACK INTO ENGLISH
I do not like to eat your cheese
That didn't even make that much sense in English.