What operation would you we to convert cups to gallon explain

We'd divide. 

This is because:

Gallons are much more than cups. If we cant to convert cups to gallons, we divide to get a smaller unit. 

Example: There are 32 cups on the table. How many gallons are there?

32/amount of cups per gallon
32/16 = 2

2 gallons, 

In a gallon there are 4 quarts. Each quart holds two pints, and each pint holds 2 cups. Therefore there are 16 cups in a gallon.
I would convert cups to gallons by dividing the number of cups by sixteen.
I would convert gallons to cups by multiplying by sixteen.