G4.4 Determine the product of all real roots of the equation $x^{4}+(x-4)^{4}=32$.
Let $t=x-2$, then the equation becomes $(t+2)^{4}+(t-2)^{4}=32$
$$
\begin{array}{l}
2\left(t^{4}+24 t^{2}+16\right)=32 \\
t^{4}+24 t^{2}=0 \\
t^{2}=0 \text { or }-24 \text { (rejected) } \\
t=0 \Rightarrow x=2
\end{array}
$$

Product of all real roots $=2$