Angle O is congruent with angle M
Angle O = (3x + 12) + (5x -2) = 8x + 10
So angle M = 8x + 10
angle L and angle O are supplementary, so L + O = 180
L + 8x + 10 = 180
L = 180 - 10 - 8x
L = 170 - 8x
The internal angles of triangle LPM are L/2, P and M/2 and they add to 180
L/2 + P + M/2 = 180
(170 - 8x)/2 + (8y -6) + (8x + 10)/2 = 180
85 - 4x + 8y -6 + 4x + 5 = 180
8y = 180 - 85 + 6 - 5
8y = 96
y = 96/8= 12
y = 12
The answer is the option D y = 12