say the 6 colors are a,b,c,d,e and f.
then, the given cases will be:
aa-bc
aa-bd
aa-be
aa-bf
aa-cd
aa-ce
... and so on.
(1) 2 same color and 2 different colors : 6 * 5C2 = 6 * 10 = 60
(2) all the cases : 12C4 = 55x9
P = (1)/(2) = 60 / (55*9) = 4 / 33
I am not 100% sure...