Answer
$$M= 36$$
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}^{4} \int_{-1}^{(2-y) / 2}\left[(y-6)^{2}+z^{2}\right] d z d y d x\\
&=\int_{-2}^{2} \int_{-2}^{4}\left[\frac{(y-6)^{2}(4-y)}{2}+\frac{(2-y)^{3}}{24}+\frac{1}{3}\right] d y d x
\end{align*}
Let
$$t=2-y,\ \ dt=-dy $$ Then
\begin{align*}
I_{L}&=4 \int_{-2}^{4}\left(\frac{133^{3}}{24}+5 t^{2}+16 t+\frac{49}{3}\right) d t\\
&=4 \left(\frac{133^{3}}{24}t+\frac{5}{3} t^{3}+8 t^2+\frac{49}{3}t\right)\bigg|_{-2}^{4} \\
&=1386
\end{align*}
Then
$$M=\frac{1}{2}(3)(6)(4)=36$$
