Subtract the nth number from the (n+1)st. You get 2, 4, 8, 14, ? Do it again for that sequence. You get 2, 4, 6, ? Maybe that sequence is 2, 4, 6, 8, 10, 12, 14, 16, 18, ... If so, then the sequence "above" it is 2, 4, 8, 14, 22, 32, 44, 58, 74, ... And the original sequence is 2, 4, 8, 16, 30, 52, 84, 128, 186, 260, ...
You just need to solve for g, multiply it out to get -g+6+2g=-4g-4, subtract 6 from both sides to get -g+2g=-4g-10, then add 4g to both sides for -g+2g-4g=-10, then add the g's together to get -3g=-10, divide both sides by -3 and you get g=3,1,3 (three and one third).