The angles that form similarity are those that are vertically opposite and 2 pairs that are equal because the for a Z formation.
Since <LPM = <ONM then
Cross multiply
12*(5x - 10) = 16*(4x - 9) Remove the brackets on both sides.
60x - 120 = 64x - 144 Subtract 60x from both sides.
- 120 = 64x - 60x - 144
-120 = 4x - 144 Add 144 to both sides.
-120 + 144 = 4x
24 = 4x Divide by 4
24/4 = x
x = 6