EG bisects angle DEF, so the two angles DEG and GEF are congruent. This means
3x + 8 = 5x - 4
Solve for x :
8 + 4 = 5x - 3x
2x = 12
x = 6
Then the measure of angle GEF is
5x - 4 = 5*6 - 4 = 26
degrees.
