A recipe for homemade clay calls for 6 cups of water for every 12 cups of flour. How many cups of water are needed when 4 cups of flour are used?

4

water : flour = 6 : 12 = 1:2

so ,
x : 4 = 1 : 2
x/4 = 1/2
x = 2

or, since you are using 1/3 of the flour you have to use 1/3 of the water,
and 1/3 of 6 cups of water = 2 cups of water