Answer
$$
I_{y z}=\frac{m}{6} a h
$$
Work Step by Step
Mass of differential element is $d m=\rho d V=\rho h x d y=\rho h(a-y) d$
$$
m=\int_m d m=\rho h \int_0^a(a-y) d y=\frac{\rho a^2 h}{2}
$$
Using the parallel axis theorem:
$$
\begin{aligned}
& d I_{y z}=\left(d I_{y^{\prime} z^{\prime}}\right)_G+d m y_G z_G \\
&=0+(\rho h x d y)(y)\left(\frac{h}{2}\right) \\
&=\frac{\rho h^2}{2} x y d y \\
&=\frac{\rho h^2}{2}\left(a y-y^2\right) d y \\
& I_{y z}=\frac{\rho h^2}{2} \int_0^a\left(a y-y^2\right) d y=\frac{\rho a^3 h^2}{12}=\frac{1}{6}\left(\frac{\rho a^2 h}{2}\right)(a h)=\frac{m}{6} a h
\end{aligned}
$$
