I need to answer with an integer or simplified fraction

Try setting up a proportion. 4 cups of flour is to 1 1/8 cups of milk as 2 cups of flour is to x (the unknown) cups of milk:

4 cups of flour 2 cups of flour

--------------------- = ----------------

(9/8) cups of milk x cups of milk

Solve for x

x = 2*9/4*8 = 9/16 cups of milk

That makes sense because 2 cups is 1/2 of 4 cups, so we should use 1/2 as much milk

(1/2)*(9/8) = 9/16