Looks spot on to me. If you only had 8 people to start with and had to form two 4 people committees there would be 8 ways to choose the first member of the first committee, then 7 ways to choose the second, then 6 to choose the third, then 5 to choose the last member of the first committee which corresponds to 8C4 and of course 4C4 is just 1. Now just add the 12C4 apply the product principle and get your answer!