How to solve this kind of question?

96 degrees.

x is the opposite angle to one of the interior angles in the quadrilateral. The interior angles to the quadrilateral are.
1. For the pentagon 180-108 = 72 degrees
2. For the hexagon 180-120 = 60 degrees
3. For the angle with both hexagon and pentagon = 360 - 180 - 120 = 132
4. For the opposite angle to x, since it's the last of the 4 angles in the quadrilateral  will be 360 - 72 - 60 - 132 = 96 degrees

And since x is opposite this 4th angle, it too will have the value 96 degrees.

Set up a system of equations