[GaryVoshol]

We'll ignore the Audience Selection for a moment. Let's assume it's from group A for the time being.

So the Red Alliance chooses one from B, one from C, and one from D.
2 x 2 x 2 = 8

They can go in position 1, 3 or 4 - there's six permutations:
B, C, D
B, D, C
C, B, D
C, D, B
D, B, C
D, C, B

8 x 6 = 48

The Blue Alliance gets to make the same choices.
48 x 48 = 2304

The Audience had 2 choices
2304 x 2 = 4608

And finally the Audience Selection could have come from 4 categories, in which case the alliances still had 48 choices each.
4608 x 4 = 18423