Answer
$(f o g)^{-1} (x)=\dfrac{x}{4}-6$
Work Step by Step
We have $f(g(x))=f(x+6)$
or, $=4(x+6)$
or, $=4x+(6)(4)$
or, $y=4x+24$
Interchanging $x$ and $y$: $x=4y +24$
$\implies \dfrac{x}{4}=y+6$
or, $y=\dfrac{x}{4}-6$
Replace $y$ with $(f o g)^{-1} (x)$
$(f o g)^{-1} (x)=\dfrac{x}{4}-6$
