The answer is 5.5 gallons. One cup is 0.0625 gallons. If each guest will drink 2 cups of punch, 20 guests will drink: 20 * 2 cups = 40 cups = 40 * 0.0625 gallons = 2.5 gallons. So, 20 guests will drink 2.5 gallons. The host had 8 gallons and after the party he will have: 8 gallons - 2.5 gallons = 5.5 gallons.