Dividing n children into classes with preferences (up to 4 preferences per child)

I have the following problem that I need to solve:
A group of n children have to be divided into two classes for the next school year. They each get to give up to four preferences of who they would like to be in class with. So I need a solution that will take into account their preferences, but also divide boys and girls equally over the two classes.

I realize this is almost like the stable marriage problem, except that there are up to four preferences here instead.
I have no idea how to solve this and with no VBA knowledge this seems impossible to solve.
Hope you guys can help me.

Thread title changed by OP. Thanks