how could I have solved this?

The fraction can be rewritten as:

15^x + 15^(x + 1) = (4^y) * (15^y)

Deal with the left side first:

15^x + 15^(x + 1) = (15^x) * (1 + 15) = (15^x) * 16 = (15^x) * (4^2)

So you have that:

(15^x)*(4^2) = (4^y)*(15^y) --- since 4^2 has to be equal to 4^y, you get y = 2. This means that:

(15^x)*(4^2) = (4^2)*(15^2) --- divide each side by 4^2 to get

15^x = 15^2 --- x = 2.