Answer
$$0$$
Work Step by Step
$$
\left|\begin{array}{rrr}{1} & {2} & {3} \\ {2} & {4} & {6} \\ {-3} & {-4} & {2}\end{array}\right|=\left|\begin{array}{rrr} {4} & {6} \\ {-4} & {2}\end{array}\right|-2\left|\begin{array}{rrr} {2} & {6} \\ {-3} & {2}\end{array}\right|+3\left|\begin{array}{rrr} {2} & {4} \\ {-3} & {-4}\end{array}\right|\\
=(8+24)-2(4+18)+3(-8+12)\\
=32-44+12=0.
$$
