Because sides are parallel, corresponding angles are congruent (angle W = angle V and angle U = angle T). By the third angle theorem (or you can use the reflexive property if that's easier), angle S = angle S. To determine triangles as similar, all angles must be congruent, and all sides must be equally proportional. This is true here because all of the angles are equal, so all of the sides must be proportional (I don't remember the theorem here)
To get the answer of x, use the proportional formula (UW/TV = US/TS). So (12/3)=(9/x), 4 = 9/x, 4x = 9, x = 9/4.
