Answer
$\det (A)=-48$
Work Step by Step
We have the cofactor expansion theorem is:
$\det (A)=a_{12}C_{12}+a_{22}C_{22}$
with $C_{ij}=(-1)^{i+j}.M_{ij}$
to evaluate the given determinant of row 2:
$\det (A)=6C_{12}+9C_{22}$
$\det (A)=6(-1)^{1+2}.M_{12}+9(-1)^{2+2}.M_{22}$
Plug in the given values:
$\det (A)=6(-1)^{1+2}.(-4)+9(-1)^{2+2}.(-8)$
$\det (A)=24+(-72)$
$\det (A)=-48$
