No, you did that when you swapped the sides!
You had -3x> -12. If you had simply divided both sides by -3 without either changing the sign or swapping sides you would have x> 4 which would be wrong. You can either change the sign, to get x< 4 or swap sides to get 4> x (your answer) but not both.
Of course, it is easy to check this yourself. A number less than 4 is 2. Does x= 2 satisfy (-3/2)x> -6?