10-|x-2|=-12------------?

10 - |x - 2| = -12
|x - 2| = 10 - (-12)
|x - 2| = 22
x - 2 = ±22

x - 2 = 22
x = 22 + 2
x = 24

x - 2 = -22
x = -22 + 2
x = -20

∴ x = -20, 24

22 = | x - 2 |

x - 2 = 22
x = 24

OR

x - 2 = - 22
x = - 20

x = - 20 , x = 24

You can do this like regular algebra, but you keep the absolute value intact until the last step.
10 - |x - 2| = -12 : original
- |x - 2| = -22 : subtract the 10 to get variable alone on left
|x - 2| = 22 : then multiply by -1 to get rid of negatives

So to solve this, set up the two equations :
x - 2 = 22: when the value INSIDE the absolute is positive
and x - 2 = -22 : when the value INSIDE the absolute is negative

So x = 24
and x = -20 <<-- your two answers

10-|x-2|=-12
10+12 = |x-2|
22 = |x-2|
x-2 = ±22
x=±22 +2
x =22+2 or x= -22+2
x=24 or x= -20

10 - |x-2| = -12
22 = |x-2|
So:
x - 2 = 22
or
x - 2 = -22

which means
x = 24
or
x = -20

-|x-2| = -22
|x-2| = 22
x-2 = +/- 22
x = 24 or x = -20

10-|x-2|=-12
-|x-2|=-22
|x-2|=22
x = -20
x = 24