Answer :
To calculate the given function:
[tex]\begin{gathered} f(x)=x^2+4x \\ g(x)=x+6 \end{gathered}[/tex](a) (fog)(x) = f(g(x))=
[tex]\begin{gathered} f(x+6)=(x+6)^2+4(x+6) \\ =x^2+12x+36+4x+24 \\ =x^2+16x+60 \end{gathered}[/tex](b) (gof)(x) = g(f(x))=
[tex]g(x^2+4x)=x^2+4x^{}+6[/tex](c) (fof)(x) = f(f(x))=
[tex]\begin{gathered} f(x^2+4x)=(x^2+4x^{})^2+4(x^2+4x) \\ =(x^2+4x)(x^2+4x)+4x^2+16x \\ =x^4+8x^3+16x^2+4x^2+16x \\ =x^4+8x^2+20x^2+16x \end{gathered}[/tex](d) (gog)(x) = g(g(x)=
[tex]\begin{gathered} g(x+6)=(x+6)+6 \\ =x+12 \end{gathered}[/tex]