Can someone explain why the hint is useful? If $\mathcal{N}_{0}$ is the Skolem hull of $M$ and a countably infinite set of indiscernibles $\mathcal{I}$, my idea is to remove one element of $\mathcal{I}$ each time to create a new Skolem hull $\mathcal{N}_{i+1}$ generated by one less indiscernible element. The problem is that there may be a non-indiscernible element in every $\mathcal{N}_{i}$ that doesn't exist in $\mathcal{M}$ so the equality doesn't hold.
A hint or solution would be appreciated.