Answer
$-12$
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
Hence here $D=2(4\cdot(-4)-0\cdot2)-(-4)(1\cdot(-4)-0\cdot(-1))+6(1\cdot2-4\cdot(-1))=2(-16)-(-4)(-4)+6(6)=-32-16+36=-12.$
