Here's the short cut of what his mistake was:
1 gallon = 4/4 quarts
3 gallons = 12/4 quarts
Billy made 3/4 quarts of juice
12/4 - 3/4 = 9/4
9 / 4 = 2 1/4
With all that has been given, Billy made 2 1/4 gallons less than he needed.
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