Theodore has 6 gallons of milk. he uses 1/2 of it to make hot chocolate. then, he uses 2/3 of the milk he has left to make cookies. how many gallons of milk does theodore have left after making hot chocolate and cookies?

Theodore firs uses 1/2 of milk to make hot chocolate: 1 - 1/2 = 1/2. So 1/2 of milk is left. After that, he uses 3/2 of the milk he has left to make cookies. It means:
1/2 - ( 2/3 * 1/2 ) = 1/2 - 1/3 = 3/6 - 2/6 = 1/6
At the end 1/6 of the milk Theodore have left.
1/6 * 6 = 1 gallon
After making hot chocolate and the cookies 1 gallon of milk Theodore have left.