Multiplication is commutative. a * b = b * a. The problem is how you define your variables. You assume that a = 2 and b = 3, independently of the division. The reality is, a = 6 / 2 = 3 because of PEMDAS rules. Then you have 3 * 3 (a * b) = 3 * 3 (b * a) = 9.
You can't just ignore the division and do commutation on the multiplication by itself. There's no such thing as "shutting the door", whatever that means.