Right of the bat, I know the measure of angle C equals 73° because of the Isosceles Base Angle Theorem. Then, due to the Triangle Sum Theorem, I know that all of the measures in the triangle must add to 180°. To find this, just subtract 73 and 73 from 180. Finally, because angle B equals (6x + 4) and 34°, just set them equal to each other to find the value of x.
180 - 73 - 73 = measure of angle B
34° = measure of angle B
6x + 4 = 34
- 4 - 4
6x = 30
6x / 6 = 30 / 6
x = 5
Hope this helps!