Not much to do here other than to compute each of these.

\[\begin{align*}\left( {f \circ g} \right)\left( x \right) & = f\left[ {g\left( x \right)} \right] = f\left[ {8 - 3{x^2}} \right] = {\left( {8 - 3{x^2}} \right)^2} - 2\left( {8 - 3{x^2}} \right) + 1 = 9{x^4} - 42{x^2} + 49\\ & \\ \left( {g \circ f} \right)\left( x \right) & = g\left[ {f\left( x \right)} \right] = g\left[ {{x^2} - 2x + 1} \right]\\ & = 8 - 3{\left( {{x^2} - 2x + 1} \right)^2} = - 3{x^4} + 12{x^3} - 18{x^2} + 12x + 5\end{align*}\]