Angles LNM and MNI are supplementary, so their measures sum to 180°. This means
∡ LNM + ∡ MNI = 180°
∡ LNM = 180° - (19x + 2)°
The sum of the interior angles of any triangle is also 180°, so
∡ LNM + ∡ NML + ∡ MLN = 180°
(180° - (19x + 2))° + (15x - 2)° + (6x)° = 180°
Solve for x (I'll omit the degree symbol):
180 - 19x - 2 + 15x - 2 + 6x = 180
2x - 4 = 0
2x = 4
x = 2
Then ∡ MNI = (15•2 - 12)° = (30 - 12)° = 18°.
