Answer
16
Work Step by Step
Use column2 as bases of operations:
$\begin{array}( \\|A|= \\ \\ \end{array}
\begin{vmatrix} 2 &-1 &6&4\\7 &2 &-2&5\\4 &-2 &10&8\\6 &1 &1&4 \end{vmatrix} $
Column operation:
$C_1+2C_2\to C_1$
$C_3+5C_2\to C_3$
$C_4+4C_2\to C_4$
$\begin{array}( \\|A|= \\ \\ \end{array}
\begin{vmatrix} 0 &-1 &1&0\\11 &2 &8&13\\0 &-2 &0&0\\8 &1 &6&8 \end{vmatrix} $
Expand using row3:
$\begin{array}( \\|A|=-(-2) \\ \\ \end{array}
\begin{vmatrix} 0 &1&0\\11 &8&13\\8&6&8 \end{vmatrix}\begin{array}( \\=(2)(-1) \\ \\ \end{array}
\begin{vmatrix} 11 &13\\8&8 \end{vmatrix} $
$|A|=-(11\times8-13\times8)=16$
