Answer:
Angle ACB = 44°
There are two ways to solve it. Both are right
Solution number 1
From triangle ABC
angle BAC = 180°-(102° +44°) = 36°
Because BG is parallel with AC
Then angle GBA = angle BAC = 34°
Another solution
The sum of angles in the shape AGBC = 360°
So angle GBC = 360 - (90 + 90 + 44 + 102) = 34°