There are $10$ people sitting in a round table. Bob and Ben have to sit opposite from each other, and Jeff and John also have to sit opposite from each other. How many possible seatings are there?
I think it should be $9 \cdot 6!$, since you can pick Bob first, and then pick Ben, leaving $9$ spots for Jeff and John to be. Then you can arrange the rest of the people in $6!$ ways.