Stacy uses 4 cups of milk to make a batch of rice pudding. How many batches of rice pudding can she make with 3 gallons of milk?

There are 16 cups in 1 gallon of milk.

So, 3 gallons of milk is equal to 3 x 16 = <<3*16=48>>48 cups of milk.

Then, Stacy can make 48/4 = <<48/4=12>>12 batches of rice pudding. Answer: \boxed{12}.