In how many ways can we seat 6 people around a round table if Fred and Gwen insist on sitting so that one person is between them? (Two seatings are considered equivalent if one is a rotation of the other.)

Let Fred and Gwynn occupy any two chairs....and they can be seated in 2 ways

The other 4 people can be seated in 4! = 24 ways

So

2 * 24 =

48 ways