R is the midpoint of PQ
So. PR = RQ
Given : PR = 3x + 6 and RQ = 5x - 2
so,
3x + 6 = 5x - 2
Solve to find the value of x
Combine like terms
3x - 5x = -2 - 6
-2x = -8
Divide both sides by -2
x = -8/-2
x = 4
PR = 3x + 6 = 3 * 4 + 6 = 12 + 6 = 18
RQ = 5x - 2 = 5 * 4 - 2 = 20 - 2 = 18
PQ = PR + RQ = 18 + 18 = 36