BBG BBG BGG BGG is our only way of splitting it up.
To make our groups, 6!*6!/2/2/2/2, but since some groups are the same, 6!*6!/2/2/2/2/2/2 = 8100.
8100 ways of making groups, 4*3*2 of giving colours.
8100*4*3*2 = 194400
Edit:
I read the question wrong, it's 3 groups of 4, not 4 groups of 3.
=^._.^=