This can only be answered if we know that segments BG, CF, and DE are parallel. I don't see that written anywhere. I'll assume that is given.
To find GF:
AG is to AB as GF is to BC
AG/AB = GF/BC
20/16 = GF/12
5/4 = GF/12
4GF = 5 * 12
4GF = 60
GF = 15
To find FE:
AG is to AB as FE is to CD
AG/AB = FE/CD
20/16 = FE/8
5/4 = FE/8
4FE = 5 * 8
4FE = 40
FE = 10