The equations of the given lines are

3x + y -2 = 0 ------ (1)

px + 2y – 3 = 0------(2)

2x – y – 3 = 0 ------ (3)

On solving equations (1) and (3), we get,

x = 1 and y = -1

Since, the three lines may intersect at one point, the point of intersection of lines (1) and (3) will also satisfy line (2).

p(1) + 2(-1) -3 = 0

=> p – 2 -3 = 0

=> p =5

Therefore, the required value of p is 5.