The different combinations of 4 children are: all boys, all girls, 2 of each, 3 of one and one of the other.
All we need to do is to work out the probability of all boys and all girls. The probability is 1/16 in each case because there is a probability of 1/2 for a boy or a girl. For all 4 children to be of the same gender the probability is (1/2)^4=1/16. So 2/16=1/8 is the probability of all boys or all girls. All the other combinations ensure that there's at least one boy and one girl. This probability is 1-1/8=7/8=0.875. In 128 families 7/8 of them=112 can be expected to contain at least one boy and one girl.