Answer
$48$
Work Step by Step
We are given the determinant:
$D=\begin{vmatrix}1&-3&2&0\\-3&-1&0&-2\\2&1&3&1\\2&0&-2&0\end{vmatrix}$
In order to compute the determinant we expand it along the fourth row because it has 2 zeros:
$D=-2D_{41}+0D_{42}-(-2)D_{43}+0D_{44}=-2D_{41}+2D_{43}$
$=-2\begin{vmatrix}-3&2&0\\-1&0&-2\\1&3&1\end{vmatrix}+2\begin{vmatrix}1&-3&0\\-3&-1&-2\\2&1&1\end{vmatrix}$
$=-2\left(-3\begin{vmatrix}0&-2\\3&1\end{vmatrix}-2\begin{vmatrix}-1&-2\\1&1\end{vmatrix}+0\right)+2\left(1\begin{vmatrix}-1&-2\\1&1\end{vmatrix}+3\begin{vmatrix}-3&-2\\2&1\end{vmatrix}+0\right)$
$=-2[-3(0+6)-2(-1+2)]+2[(-1+2)+3(-3+4)]$
$=-2(-20)+2(4)=48$