In how many ways can 3 boys and 3 girls be seated in a row if the row begins and ends with a boy

The first and last seat must be taken by boys, so there are 3 boys to choose from for the first seat and 2 boys to choose from for the last seat. The remaining 4 seats can be filled by the 3 girls in 4! = 24 ways.

Therefore, the total number of ways the 3 boys and 3 girls can be seated in a row if the row begins and ends with a boy is 3 * 2 * 24 = 144 ways.