Answer
$\text{$x-$intercepts: } \{
6, 2 \}
$
Work Step by Step
Setting $y=0$ and solving for $x$ using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), then the $x-$intercept/s of the given equation, $
y=-x^2+8x-12
,$ is/are
\begin{array}{l}\require{cancel}
-x^2+8x-12=0
\\\\
x=\dfrac{-8\pm\sqrt{8^2-4(-1)(-12)}}{2(-1)}
\\\\
x=\dfrac{-8\pm\sqrt{64-48}}{-2}
\\\\
x=\dfrac{-8\pm\sqrt{16}}{-2}
\\\\
x=\dfrac{-8\pm\sqrt{(4)^2}}{-2}
\\\\
x=\dfrac{-8\pm4}{-2}
.\end{array}
Hence, the $x-$intercepts are
\begin{array}{l}\require{cancel}
\text{$x-$intercepts: } \{
6, 2 \}
.\end{array}
