The problem is to express the probability-generating function in terms of moment-generating function. I'm not sure how to approach this. Is it saying to find the MGF of the probability generating function or to give the MGF that corresponds to the PGF?
Probability generating function is
$$G(s)=\sum _k s^kp_k$$
If $X$ is a random variable taking values in the non-negative integers, then its probability generating function is $$ \Phi_X(s)=\sum_{n=0}^{\infty}\mathbb{P}(X=n)s^n=\mathbb{E}[s^X]$$ On the other hand, the moment generating function for $X$ is $$ M_X(t)=\mathbb{E}[e^{tX}]=\sum_{n=0}^{\infty}\mathbb{P}(X=n)e^{tn} $$ Comparing the two, we see that $$ M_X(t)=\Phi_X(e^t)$$ or $$ \Phi_X(s)=M_X(\log s)$$ if $s>0$.