help me solve for x please?

x² - 3x + 2 = 0
(x - 2)(x - 1) = 0
x = 2 , x = 1

6x^2 - 18x + 12 = 0
(6x^2 - 18x + 12)/6 = 0/6
x^2 - 3x + 2 = 0
x^2 - x - 2x + 2 = 0
(x^2 - x) - (2x - 2) = 0
x(x - 1) - 2(x - 1) = 0
(x - 1)(x - 2) = 0

x - 1 = 0
x = 1

x - 2 = 0
x = 2

∴ x = 1 , 2

The first step was correct.
6(x^2 - 3x + 2) = 0
Since 6 can not be equal to zero, (x^2 - 3x + 2) = 0
These equations are termed as Quadratic Equations.
Take up the whole of (x^2) term and the constant term (+2).
Now multiply them to get 2 * (x^2).
You have to split 2*(x^2) into two factors each containing a 'x' term.
When we add these two factors we should get the 'x' term in the equation i.e., (-3x).
Now 2*(x^2) can be split into (-2x) and (-x). When we multiply them we get 2*(x^2) and when we add them we get -3x.
Replace -3x by (-2x) + (-x)
x^2 - 3x + 2 = 0
=> x^2 -2x -x +2 = 0
=> x(x-2) - 1(x-2) = 0
=> (x-2) * (x-1) = 0
=> x=1, x=2.

6x^2-18x+12=0
6x^2 - 12x - 6x + 12 = 0
6x(x - 2) - 6(x-2)=0
(6x-6)(x-2)=0
Which means that
6x - 6 = 0 OR x -2 =0
=> x = 1 OR x = 2

You need to factor:

6(x-1)(x-2) = 0

So your answers are 1 and 2.