This matrix element is given by $$ \langle ^{16}\mathrm{O}|a_ba_a\frac{1}{4}\sum_{pqrs}\langle (pq) M | \hat{V} | (rs) M' \rangle a^{\dagger}_pa^{\dagger}_qa_sa_r a^{\dagger}_ca^{\dagger}_d|^{16}\mathrm{O}\rangle. $$ We can compute this matrix element using Wick's theorem.