There are 8 cups in half of one U.S. gallon. This means that a half gallon is also equivalent to 2 quarts. In the U.S., milk and other liquids are often sold in standard half-gallon or gallon jugs.
Another gallon measurement is the dry gallon, which is used mostly in America. One dry gallon equals around 1.16 U.S. gallons, and therefore a half of a dry gallon equals around 9.3 cups.
The British have a measurement called the imperial gallon, which is quite different from the American gallon. One imperial gallon equals roughly 1.20 U.S. gallons, and therefore one-half of an imperial gallon equals about 9.6 U.S. cups.