All you need is 4 black pawns taking white pieces and passing the white pawns. Consider the formation.
White pawns at a2, b3,
Black pawns at a3, b4,
First let the black pawns at a3 take white piece at b2. Then white pawn b3 takes a black piece at a4. Now black queens both the pawn in b-file and white queens both the pawn in a-file.
It is theoretically possible. Only for academic interest
Is it possible to have 18 queens on the board?
Problem: how does every single pawn pass each other and get to the other side?
Lol if anyone has solved it i'd really like to see the game. =]