Line m is represented by the equation y + 2 = 3/2(x + 4). Last one just to make sure of something here.

The slope of the given line = m = 3/2    perpindicular  is  - 1/m  = -2/3

   which answer(s) have slope = -2/3 ????

When the equation is in this form ( where the coefficient of  y  is  1 ),

we can pick off the slope of the line as the coefficient of  x .

 

Here, the coefficient of  x  is  $\frac32$   so

 

slope of line  m   =   $\frac32$

 

And...

 

slope of line perpendicular to  m  =  the negative reciprocal of  $\frac32$

 

slope of line perpendicular to  m  =  $-\frac23$

 

The equations that have  $-\frac23$  (or something equaivalent to  $-\frac23$ ) as the coefficient of  x  represent lines perpendicular to  m