Answer
$54$
Work Step by Step
The elements of the first row are $3, 6$ and $-3$. The first row of the array of signs is $ + , - , +$ .
$$\begin{vmatrix}
3 & 6 & -3\\
-1 & -2 & 3\\
4 & -1&6
\end{vmatrix}=3\begin{vmatrix}
-2 & 3 \\
-1 & 6
\end{vmatrix}-6\begin{vmatrix}
-1 & 3 \\
4& 6
\end{vmatrix}-3\begin{vmatrix}
-1 & -2 \\
4& -1
\end{vmatrix}$$
$$=3(-12+3)-6(-6-12)-3(1+8)=-27+108-27=54$$
