First thing is to find the slope of the perpendicular line.
Slope of 2x -3y = 9
-3y = 9 - 2x
y = -3 +(2/3)x
y = (2/3)x - 3
slope = 2/3
Perpendicular is opposite sign, flipped fraction
slope perpendicular = -3/2
...contains the point (-6,12)
point-slope form...
y - y1 = m (x - x1)
y - 12 = (-3/2) (x + 6)
y - 12 = (-3/2)x - 9
y = (-3/2)x + 3