If $|G| = p^nq$, with $p\gt q$ primes, then $G$ contains a unique normal subgroup of index $q$.
Why does author mention both unique and normal? Subgroup of index $q$ is Sylow $p$-subgroup of $G$. So uniqueness $\iff$ normality. Showing uniqueness is relatively easy compared to normality. Here is proof of above exercise showing uniqueness.