Answer
$15$
Work Step by Step
The determinant of the matrix is the same regardless of the row or column you select to expand by.
Choosing the first row:
The elements of the first row are $1, 0$ and $4$. The first row of the array of signs is $ + , - , +$ .
$$\begin{vmatrix}
1 & 0 & 4\\
1 & -1 & 2\\
3 & 2&1
\end{vmatrix}=1\begin{vmatrix}
-1 & 2 \\
2 & 1
\end{vmatrix}-0\begin{vmatrix}
1 & 2 \\
3& 1
\end{vmatrix}+4\begin{vmatrix}
1 & -1 \\
3& 2
\end{vmatrix}$$
$$=1(-1-4)-0(1-6)+4(2-(-3))=-5-0+20=15$$