Answer
If $f\left( g\left( x \right) \right)=-\frac{3}{g\left( x \right)-4}$ and $g\left( x \right)=\frac{8}{x}$ then 0 and $2$ must be excluded from the domain of $f\circ g$.
Work Step by Step
Consider the given expressions:
$f\left( g\left( x \right) \right)=-\frac{3}{g\left( x \right)-4}$
And
$g\left( x \right)=\frac{8}{x}$
Substitute $g\left( x \right)$ in the above expression,
$f\left( g\left( x \right) \right)=-\frac{3}{\frac{8}{x}-4}$
Hence, the real numbers that are to be excluded from the expression will be $0$ and $2$.
