Answer
$\text{$y-$intercept: }
-12$
Work Step by Step
Setting $x=0$ and then solving for $y$, then the $y-$intercept of the given equation, $
y=-x^2+8x-12
,$ is
\begin{array}{l}\require{cancel}
y=-(0)^2+8(0)-12
\\\\
y=-0+0-12
\\\\
y=-12
.\end{array}
Hence, the $y-$intercept is
\begin{array}{l}\require{cancel}
\text{$y-$intercept: }
-12
.\end{array}