In how many ways can we seat 6 people at a round table if John and Sam insist on sitting next to each other? (Two seatings are equivalent if one is a rotation of the other.)
To take care of rotations, we can fix John at the topmost seat.  We then have two choices for Sam: either side of John. The other four may sit anywhere in the other four seats. Thus there are $2\times 4! = \boxed{48}$ ways.