Answer
(a) Expansion by cofactors of the third row, we have
\begin{align*}
\left|\begin{array}{rrr}{-3} & {2} & {2} \\ {4} & {5} & {6} \\ {2} & {-3} & {1}\end{array}\right|
&=4C_{31}-7C_{32}-8C_{33}\\
&=4(-2)-7(15)-8(-33)\\
&=8-14+184\\
&=151.
\end{align*}
(b) Expanding by the first column, we have
\begin{align*}
\left|\begin{array}{rrr}{-3} & {2} & {2} \\ {4} & {5} & {6} \\ {2} & {-3} & {1}\end{array}\right|
&=-3C_{12}+6C_{21}+4C_{31}\\
&=-3(-17)+6(18)+4(-2)\\
&=51+108-8\\
&=151.
\end{align*}
Work Step by Step
Given
$$
\left|\begin{array}{rrr}{-3} & {4} & {2} \\ {6} & {3} & {1} \\ {4} & {-7} & {-8}\end{array}\right|.
$$
The cofactors, are given by:
\begin{align*}
C_{11}&=-17, \quad C_{12}=52, \quad C_{13}=-54,\\
C_{21}&=18, \quad C_{22}=16, \quad C_{23}=-5,\\
C_{31}&=-2, \quad C_{32}=15, \quad C_{33}=-33.
\end{align*}
(a) Expansion by cofactors of the third row, we have
\begin{align*}
\left|\begin{array}{rrr}{-3} & {2} & {2} \\ {4} & {5} & {6} \\ {2} & {-3} & {1}\end{array}\right|
&=4C_{31}-7C_{32}-8C_{33}\\
&=4(-2)-7(15)-8(-33)\\
&=8-14+184\\
&=151.
\end{align*}
(b) Expanding by the first column, we have
\begin{align*}
\left|\begin{array}{rrr}{-3} & {2} & {2} \\ {4} & {5} & {6} \\ {2} & {-3} & {1}\end{array}\right|
&=-3C_{12}+6C_{21}+4C_{31}\\
&=-3(-17)+6(18)+4(-2)\\
&=51+108-8\\
&=151.
\end{align*}
