I need step-by-step answers so I can fully understand.

First get the equation in slope-intercept form (y=mx+b, where m=slope):

3x - 2y + 4 = 0

-3x -3x

-2y +4 = -3x

-4 -4

-2y =
-3x - 4

-2 -2 -2

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

y = (3/2)x + 2

The slope of the line for this equation is the number multiplied to the x. So, m (slope) is 3/2.

Now, a perpendicular slope will be the negative reciprocal. The negative recipriocal of 3/2 = -2/3.