Calculating Standard Gibbs Energy of Dissolution
You are correct that you need $\Delta G^\circ =-RT\ln{K}$ and that the equilibrium constant in this case is $K_{sp}$ the solubility product constant, which is defined for a process like this one to be:

$$\ce{A_{m} B_{n} (s) &lt;=&gt; mA^{n+}(aq) + nB^{m-}(aq)}$$
$$K_{sp} = \ce{[A^{n+}]^{m} [B^{m-}]^{n}}$$

In your case $K_{sp}=[\ce{Hg2^{2+}}][\ce{I-}]^2$

You are given the solubility (maximum obtainable concentration) of $\ce{Hg2I2}$ in water at $25 \ ^\circ \text{C}$. How can you use that information to find $[\ce{Hg2^{2+}}]$ and $[\ce{I-}]$ when the solution is saturated?