For f(g(x)) the answer is
[tex]f((x-2)^{3} +4) = \sqrt[3]{x^{3} -6x^{2}+12x-1 }[/tex]
For g(f(x)) the answer is
[tex]g(\sqrt[3]{x +3} = x-1-6\sqrt[3]{(x+3^{2} } + 12\sqrt[3]{x+3}[/tex]
You just need to set up the composition and evaluate.
Hope this helpsʕ•ᴥ•ʔ