My approach would be to solve for -2/3X = 6. To accomplish this you want to isolate X on one side of the equation (e.g. X=) and have a number on the other side of the equation., In this instance, in order to get X by itself on one side of the equation we need to divide both sides of the equation by -3/2 because a fraction multiplied by its own inverse (e.g. 2/1 x 1/2) equals 1. In order to keep an equation valid, whatever we do to one side of the equation we need to do to the other side as follows:

(-3/2) (-2/3) X = (6/1)(-3/2)

Note; a minus multiplied by another minus number gives you a plus value so (-2/3)(-3/2) = +1 but (6) (-3/2) gives you a negative number.

Multiplying both sides out we get:

+1X (or just X) = -18/2

further simplification gives us:

X= -9

Thus X > -9 

Multiply both sides of the inequality by the reciprocal of the fractional coefficient of the variable x (i.e., multiply both sides by -3/2). Since you are multiplying by a negative number, and thus changing the signs, you must also flip the inequality symol:

(-2/3)x < 6   »»»   (-3/2)*(-2/3)x > (6)*(-3/2)   

                      »»»   ((-3*-2)/(2*3))x > (6*-3)/(2)

                      »»»   (6/6)x > (-18/2)   »»»   (1)x > (-9)

                      »»»   x > -9

If your inequality is: (-2/3)x < 6, then you just need to multiply both sides by the reciprocal of -2/3.  Since you're multiplying by a negative number, you need to flip the inequality sign:

(-3/2)(-2/3)x > 6(-3/2)

Now, simplify:  

x > -9

Finally, you may need to graph the solution in the number line.  Can you do that?  I'm sure you can!