You were doing okay until the last line, where you forgot 6*4 = 24

In the line before the last, you should have removed the 4 from y/4.

So your initial equation is

y = 4x^2 -24x +12

Then,

y = 4[x^2 -6x +3]

This has to be done so that the coefficient of the x^2 is 1 only, because completing squares is done when the coefficient of the squared variable is 1 only.

Then, following your style,

y = 4[x^2 -6x +9 +3 -9]

y = 4[(x-3)^2 -6]

y = 4(x-3)^2 -24