Answer
$$36$$
Work Step by Step
The plane $y+2 z=2$ is the top of the wedge
\begin{align*}
I_{L}&=\int_{-2}^{2} \int_{-2}^{4} \int_{-2}^{(2-y) / 2}\left[(x-4)^{2}+y^{2}\right] d z d y d x\\
&= \frac{1}{2} \int_{-2}^{2} \int_{-2}^{4}\left(x^{2}-8 x+16+y^{2}\right)(4-y) d y d x\\
&=\int_{-2}^{2}\left(9 x^{2}-72 x+162\right) d x\\
&=\left(3 x^{3}-36 x^2+162x\right)\bigg|\\
&=696
\end{align*}
Then
$$M=\frac{1}{2}(3)(6)(4)=36$$
