The quick way to solve this type of problem is to learn that the
equation of a line:

1. parallel to Ax + By = C through (x1, y1) is
   Ax + By = Ax1 + By1

2. perpendicular to Ax + By = C through (x1, y1) is 
   Bx - Ay = Bx1 - Ay1

So the answer is 3x - 2y = 3(-4) - 2(4)
                 3x - 2y = -12 - 8
                 3x - 2y = -20

But often this method is not taught.  So we find the slope of
2x + 3y = 8 by solving for y to get it into slope-intercept form
y = mx + b:

2x + 3y = 8
     3y = -2x + 8
      y = (-2/3)x + 8/3

Then we compare that to 
      y = mx + b

and get that the slope m = -2/3. Then we take the reciprocal of the
slope and give it the opposite sign, m = +3/2.  Then we use the point-
slope form for the equation of a line, which is

 y - y1 = m(x - x1)

  y - 4 = (3/2)(x - (-4))
  y - 4 = (3/2)(x + 4)
Multiply both sides by 2
 2y - 8 = 3(x + 4)
 2y - 8 = 3x + 12
2y - 3x = 20

That's equivalent to the answer using the short method. We multiply
through by -1:

-2y + 3x = -20

Then reverse the terms on the left

 3x - 2y = -20

Edwin