In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?
Name the 3 pairs of siblings: A1 and A2, B1 and B2, C1 and C2
1 - A1 has 6 choices. A2-his/her sibling has 5 - 1 =4 choices
2 - B1 has the remaining 4 choices. B2 - his/her sibling has 3 - 1=2 choices.
3 - C1 and C2 have the last 2 choices.
Total number of ways: 6 x 4 x 4 x 2 x 2 =384 ways of seating the 3 pairs.