The total number of 6 people committees out of  8 + 7 = 15 people is:

C(15, 6) = 15!/(6!(15-6)!)

C(15, 6) = 15!/(6!9!)

C(15, 6) = 10*11*12*13*14*15/6!

C(15, 6) = 5005

The number of possible selections of 2 democrats out of set of 8 is:

C(8, 2) = 8!/(2!(8-2)!)

C(8, 2) = 8!/(2!6!)

C(8, 2) = 18

The number of possible selections of 4 republicans out of set of 7 is:

C(7, 4) = 7!/(4!(7-4)!)

C(7, 4) = 7!/(4!3!)

C(7, 4) = 35

The probability of selecting two Democrats and four Republicans is:

p = (C(8, 2)*C(7, 4))/C(15, 6)

p = 18*35/5005

p = 0.1259

The probability of selecting two Democrats and four Republicans is 0.1259.