Answer
$$
M_y=282 \mathrm{lb} \cdot \mathrm{ft}
$$
Work Step by Step
Using $x^{\prime}, y^{\prime}, z$ :
$$
\begin{aligned}
\mathbf{u}_y & =-\sin 30^{\circ} \mathbf{i}^{\prime}+\cos 30^{\circ} \mathbf{j}^{\prime} \\
\mathbf{r}_{A C} & =-6 \cos 15^{\circ} \mathbf{i}^{\prime}+3 \mathbf{j}^{\prime}+6 \sin 15^{\circ} \mathbf{k} \\
\mathbf{F} & =80 \mathbf{k} \\
M_y & =\left|\begin{array}{ccc}
-\sin 30^{\circ} & \cos 30^{\circ} & 0 \\
-6 \cos 15^{\circ} & 3 & 6 \sin 15^{\circ} \\
0 & 0 & 80
\end{array}\right|=-120+401.53+0 \\
M_y & =282 \mathrm{lb} \cdot \mathrm{ft}
\end{aligned}
$$
Now, using $x, y, z$ :
The coordinates of point $C$ :
$$
\begin{aligned}
x & =3 \sin 30^{\circ}-6 \cos 15^{\circ} \cos 30^{\circ}=-3.52 \mathrm{ft} \\
y & =3 \cos 30^{\circ}+6 \cos 15^{\circ} \sin 30^{\circ}=5.50 \mathrm{ft} \\
z & =6 \sin 15^{\circ}=1.55 \mathrm{ft} \\
\mathbf{r}_{A C} & =-3.52 \mathbf{i}+5.50 \mathbf{j}+1.55 \mathbf{k} \\
\mathbf{F} & =80 \mathbf{k} \\
M_y & =\left|\begin{array}{ccc}
0 & 1 & 0 \\
-3.52 & 5.50 & 1.55 \\
0 & 0 & 80
\end{array}\right|=282 \mathrm{lb} \cdot \mathrm{ft}
\end{aligned}
$$
