How do you find the possible range of values for x ?

 if two legs of two triangles are congruent, then the angle opposite the longer side is larger. In this picture, the 60 degree angle is opposite a side of length 20. the (4x+8) angle is opposite a side of length 32. This means that the (4x-8) angle is larger than the 60 degree angle. You should also know that there are 180 degrees in a triangle, so the (4x-8) angle cannot be more than 180 degrees, therefore it must be between 60 and 180: 60 < 4x-8 < 180. 
you can solve this, or write it as two separate inequalities: 4x-8 > 60, and 4x-8 < 180. 
solve the first one to get x >17, and solve the second to get x < 47. Writing them as one expression: 

Iagree that is the answer to the question