notice, is really the same. All we do is, "insert one function into the other".
so, a way to do it is, get the value of the first one, then insert that output into the second.
[tex]\bf \begin{cases}
f(x)=-x+8\\
g(x)=x^4\\
(g\circ f)(x)=g(~~f(x)~~)
\end{cases}
\\\\\\
(g\circ f)(2)=g(~~f(2)~~)
\\\\\\
f(2)=-(2)+8\implies \boxed{f(2)=6}
\\\\\\
g(~~f(2)~~)\implies g\left(~~\boxed{6}~~ \right)\implies g(6)=(6)^4\implies g(6)=1296[/tex]