jmc

Within the conference, there are 8 teams, so there are $\left(\genfrac{}{}{0ex}{}{8}{2}\right)=28$ pairings of teams, and each pair must play two games, for a total of $28\cdot 2=56$ games within the conference. Each team also plays 4 games outside the conference, and there are 8 teams, so there are a total of $4\cdot 8=32$ games outside the conference. Therefore, the total number of games is $56+32=\boxed{88}$, so $\boxed{88}$ is our answer.