It should be -3(x-4) because the negative sign will also be distributed so it will be equal to -3x+12 which is what is in the original equation.
You made a mistake in grouping the terms here: (x² - 4x) - (3x +12) = 0
You should've included the negative sign for 3x:
(x² - 4x) + (-3x +12) = 0
or changed +12 to -12 since you initially factored out the - sign:
(x² - 4x) - (3x -12) = 0
Any of these two would've given you the right answer :)
If you used -3(x+4), that will be equal to -3x -12, which is not similar to the equation.
Btw, i like how you factor :) It's different from how a typical high school student does it