Explanation

Factor: 4p²+4pq−3q² = (2p+3q)(2p−q) = 12(2p−q) = 126, so 2p−q = 21/2. Together with 2p+3q = 12 this gives q = 3/8. Then p+2q = (2p+4q)/2 = (12+q)/2 = 99/16 (option D).