Assume family consists of Mom, Dad, 2 boys and 2 girls. If all genders alternate then MDGBGB fits that arrangement. So does DMBGBG. The children can be arranged B1G1B2G2, B2G1B1G2, B2G2B1G1, B1G2B2G1 and four arrangements with the genders reversed. Combined with M and D we therefore have 8 arrangements. But there are 6 seating positions around the table so in total there are 6*8=48 arrangements.