What is the value of p if the line (3p + 1)x - 2y = 6p is perpendicular to the line 2x - y + 1 = 0

2x-y+1=0 has slope 2

so, the desired line needs slope -1/2

so, 3p+1 = -1
p = -2/3
(the 6p on the other side of the equation is irrelevant)