Billy is making a juice that contains 3 quarts of water, 1 quart of grape juice, 1 quart of orange juice, and 2 quarts of strawberry juice. he is putting his homemade juice into a jug that can hold 2 1⁄2 gallons. how many more quarts of juice can billy still make before filling the jug?

We have that
Billy is making a juice that contains
3 quarts of water
1 quart of grape juice
1 quart of orange juice
2 quarts of strawberry juice
total=3+1+1+2> 7 quarts

a jug  can hold 2 1⁄2 gallons> 2.5 gallons

we know that
1 gallon is equal to 4 quarts
2.5 gallons> x
x=2.5*4> x=10 quarts
so

quarts of juice can Billy still make before filling the jug=10-7---> 3 quarts

the answer is
3 quarts