The first team (boy,girl) can be arranged in 7*5 = 35 ways.
After that, the second team (boy,girl) can be arranged in 6*4 = 24 ways.
Such teams can be combined in = 35*12 = 420 different ways for a game. ANSWER
Probability is an area of mathematics where it is useful to know different methods for solving a problem.
Here is an alternative to the (perfectly good) method shown by the other tutor.
(1) Choose 2 of the 7 boys in C(7,2) = 21 ways
(2) Choose 2 of the 5 girls in C(5,2) = 10 ways
(3) Make 2 teams each with one boy and one girl in 2 ways