Perpendicular lines have slopes that are negative reciprocals.

Meaning, m1 = -1/m2

or, m2 = -1/m1.

So we find first the slope of the known line:

2x -3y = 12

Transform it to y = mx +b,

-3y = -2x +12

y = (-2 / -3)x +12/(-3)

y = (2/3)x -4

So, its slope is 2/3.

Then, the slope of the unknown line is -3/2.

The slope-intercept form (or y = mx +b) of its equation then is

y = (-3/2)x +b

Since this unknown line is passing through point (4,3), then,

3 = -(3/2)*4 +b

3 = -6 +b

3+6 = b

b = 9

Therefore, the unknown line is

y = -(3/2)x +9 ----answer.