Answer
$\dfrac{x}{4}-6$
Work Step by Step
Interchange $x$ and $y$: $x=4y $
$\implies y=\dfrac{x}{4}$
Replace $y$ with $f^{-1} (x)$
or, $f^{-1} (x)=\dfrac{x}{4}$
Replace $g(x)$ with $y$.
$ g(x) =x+6$
Interchange $x$ and $y$: $x=y+6 $
so, $y=x-6 \implies g^{-1} (x)=x-6$
Now, $ g^{-1}(f^{-1} (x))=g^{-1} (\dfrac{x}{4})$
or, $=\dfrac{x}{4}-6$
or, $=(f(g(x)))^{-1}$
