Answer
See below
Work Step by Step
Given $$ A=\left[ \begin{array}{cccc}{-2} & {-1} & {4} & {-6} \\ {0} & {1} & {0} & {2} \\ {0} & {-6} & {3} & {2} \\ {0} & {8} & {5} & {1}\end{array} \right]$$
since,if we have
\begin{aligned}A =\left[\begin{array}{lll}{a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}}\\a_{41} &
a_{42} & a_{43}\end{array}\right]
\end{aligned}
So, we get
$det (A)=\begin{vmatrix} -2 & -1 & 4 & -6\\ 0 & 1 & 0 & 2\\ 0 & -6 & 3 & 2 \\ 0 & 8 & 5 & 1 \end{vmatrix}\\
=(-2).1.3.1+(-1).0.2.0+4.2.0.8-0.(-6).0.(-6)-8.3.2.(-2)-5.2.0.(-1)\\
=-6+0+0+0+0-0+96-0\\
=90$
