Order? In multiplication? You should not care about order in multiplication since A·B = B·A for any 2 numbers!

So A·B·C·6·Q·77= 77·6·C·A·B·Q = B·Q·77·C·A·6 = ...,etc.

Also when you want to multiply x-3 with 4 with 2(x-3) the result: x-3·4·2(x-3) is not correct since in that way you do not multiply x-3 with 4 but you multiply only 3 with it. Remember that 5-3·2 = 5-6 = -1 and NOT 5-3·2 = 2·2 = 4

So you should put brackets to x-3 to make it be multiplied with 4 so the right way to write it, is (x-3)·4·2(x-3)

Yes. (x-1)·4·(x+2) or 4(x-1)(x+2) is the correct product which happens to be the LCM also(for unknown variables).Lets just assume that the denominators are now $\displaystyle x-1 , 4$ and $\displaystyle x+2$ can we simply just multiply all these together?