Answer
$-4$
Work Step by Step
We know that by definition if $y=a^x$, then $log_a {y}=x$. Also $log_e {x}=ln {x}$,
and $\log_a{xy}=\log_a{x} +\log_a{y}$ hence if $y=e^x$, then $ln{e^x}=x\cdot log_e {e}=x$.
Therefore if $ln {e^{-2x}}=8$, then $-2x=8\\x=-4.$