The ilustration is below
Now the trouble that I have is to understand the limits on the integrals to solve this problem. The answer is:
$\int_0^{1/2} \int_y^1 f_1(x) \: f_2(y)\: dx\:dy = \int_0^{1/2} \int_y^1 1 \cdot \: 8y\: dx\:dy$
$y$ is on the interval $0<y<1/2$, so this is why the first integral goes from $0$ to $1/2$. But why the second integral goes from $y$ to $1$? I have some problems to understand questions like this one.