What is the equation of the line that passes through (–2, 4) and is perpendicular to 2x + 3y = –6?

So you want to get it to slope intercept for.
y = (-2/3)x -2
when you want a perpendicular slope, the slope has to be flipped including the sign. 
y = 3/2x
this is the slope now
now you want to find the y intercept, y = mx + b
4 = 3/2 * -2 + b
4 = -3 + b 
7 =  b
y = (3/2)x + 7