In the given image you can notice that angles ∠TWS and ∠RWU are congruent (because they are consecuence of the intersection of two lines in one point). It means that the measure of both angles are equal.
If m∠TWS = 108° and m∠RWU = 6x, you have:
m∠TWS = m∠RWU
108 = 6x divide by 6 both sides
108/6 = x
x = 18
Hence, the value of x is x = 18