hi
(x-2) + 4 = 12
substract 4 on both side, which is the correct thing to do.
(x-2)=8
here we can infer either a division by 4 , or substraction of 6 on the right side. Any case, rule of equation says you have to do operation on both side on the same time. So after that, it's no longer correct as not done on both side. more over, it has no utility as it does not simplify anything.
x-2=2
Assuming previous line is correct, adding +2 on both side is the correct thing to do. But as precedent step is wrong , it will not lead to a correct result.
x=4
You can see if a result is correct, by testing the value found for "x" in first line.
As ( (4) -2) +4 = 2+4 = 6
it does not match our first line who says that (x-2) +4 = 12.
So result X =6 is wrong
Now let write correct step .
I will put in bold operation and quantities used.
(x-2) +4 = 12
substract 4 on both side
(x-2) +4 -4 = 12 -4
(x-2) = 8
we no longer need the parenthesis
so let's remove
x-2 = 8
now we add 2 on both side
x-2 +2 = 8 +2
x = 10
If you had done no error , result will match first line
let's check if it works for x = 10
( 10 -2) +4 = 8+4 = 12
result match first line who state : (x-2) +4 = 12 so answer x = 10 is correct solution.