Answer
$I_y=341in^4$
Work Step by Step
We can find the required moment of inertia as follows:
$I_y=\Sigma (I+Ad^2_x)$
$\implies I_y=\frac{bh^3}{12}+Ad^2_x$
We plug in the known values to obtain:
$I_y=\frac{4(1)^3}{12}+4(1)(0.5)^2+\frac{1(6^3)}{12}+4(1)(6)^2+\frac{4(1)^3}{12}+4(1)(7.5)^2$
This simplifies to:
$I_y=341in^4$