Answer
$$
M_P=\{-60 \mathbf{i}-26 \mathbf{j}-32 \mathbf{k}\} \mathrm{kN} \cdot \mathrm{m}
$$
Work Step by Step
The coordinates of points $A$ and $P$ are $A(1,-2,6) \mathrm{m}$ and $P(0,4,3) \mathrm{m}$, respectively
$$
\begin{aligned}
\mathbf{r}_{P A} & =(1-0) \mathbf{i}+(-2-4) \mathbf{j}+(6-3) \mathbf{k} \\
& =\{\mathbf{i}-6 \mathbf{j}+3 \mathbf{k}\} \mathrm{m}
\end{aligned}
$$
The moment of $F$ About Point $P$.
$$
\begin{aligned}
M_P & =\mathbf{r}_{P A} \times \mathbf{F} \\
& =\left|\begin{array}{ccc}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
1 & -6 & 3 \\
-6 & 4 & 8
\end{array}\right| \\
& =\{-60 \mathbf{i}-26 \mathbf{j}-32 \mathbf{k}\} \mathrm{kN} \cdot \mathrm{m}
\end{aligned}
$$
