I'm not sure what your teacher means by "must use inverse operations".
Anyways, Amy uses 13% of the total milk (6 gallons). So she uses 0.13*6 = 0.78 gallons.
Then we're told that Dan used 0.14 of the total milk. So 0.14*6 = 0.84 to indicate Dan used more than Amy. Dan also used more than Mike because 0.84 gallons is larger than 0.5 gallons.