Answer
$\text{a) }
f(g(x))=8x+29
\\\text{b) }
g(f(x))=8x+16$
Work Step by Step
$\bf{\text{Solution Outline:}}$
With
\begin{array}{l}\require{cancel}
f(x)=
4x+5
\\g(x)=
2x+6
,\end{array}
to find $
f(g(x))
,$ replace $x$ with $g(x)$ in $f.$ To find $g(f(x)),$ replace $x$ with $f(x)$ in $g.$
$\bf{\text{Solution Details:}}$
Replacing $x$ with $g(x)$ in $f$, then
\begin{array}{l}\require{cancel}
f(g(x))=f(2x+6)
\\\\
f(g(x))=4(2x+6)+5
\\\\
f(g(x))=8x+24+5
\\\\
f(g(x))=8x+29
.\end{array}
Replacing $x$ with $f(x)$ in $g$, then
\begin{array}{l}\require{cancel}
g(f(x))=g(4x+5)
\\\\
g(f(x))=2(4x+5)+6
\\\\
g(f(x))=8x+10+6
\\\\
g(f(x))=8x+16
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(g(x))=8x+29
\\\text{b) }
g(f(x))=8x+16
.\end{array}
