Answer
$-3$
Work Step by Step
The elements of the first row are $2, -2$ and $1$. The first row of the array of signs is $ + , - , +$ .
$$\begin{vmatrix}
2& -2 & 1\\
4 & 1 & 3\\
3 & 1&2
\end{vmatrix}=2\begin{vmatrix}
1& 3 \\
1 & 2
\end{vmatrix}-(-2)\begin{vmatrix}
4 & 3 \\
3& 2
\end{vmatrix}+1\begin{vmatrix}
4 & 1 \\
3& 1
\end{vmatrix}$$
$$=2(2-3)-(-2)(8-9)+1(4-3)=-2-2+1=-3$$