#### Answer

-5

#### Work Step by Step

We use Cramer's rule to find the determinant of the matrix. Doing this, we obtain:
$$ \det \begin{pmatrix}-4&-2&3\\ -3&1&2\\ 3&4&-2\end{pmatrix}\\ -4\cdot \det \begin{pmatrix}1&2\\ 4&-2\end{pmatrix}-\left(-2\right)\det \begin{pmatrix}-3&2\\ 3&-2\end{pmatrix}+3\cdot \det \begin{pmatrix}-3&1\\ 3&4\end{pmatrix}\\ -4\left(-10\right)-\left(-2\right)\cdot \:0+3\left(-15\right) \\ -5$$