Make a picture of the problem.
Fred and Gwen are seated opposite each other, and we name the 4 remaining seats 1, 2, 3, 4, starting from the right of Fred.
There are 4 options for seat 1,
then 3 for the seat 2, after one is seated in the 1.st seat
2 options for the seat 3,
and 1 for the seat 4.
That is, the 4 friends can sit in 4*3*2*1=24 different ways.
Answer: 24
