Well,
-24 + 12 = -x
-12 = -x
12 = x
x= 12
1) The original equation.
2) -24 + 12 is equal to -12. Do you understand this part? If you're just learning them, adding negative and positive numbers can be tricky!
3) If you were looking for the value of -x (NEGATIVE x) then you would stop at number 2, BUT in almost EVERY case you will want to solve for x (POSITIVE x). You have probably learned that multiplying two negative numbers together results in a positive number. In this step I multiplied both sides of the equal sign by (-1). You can do anything you want to an equation as long as you do the same thing on both sides of the equal sign. I multiplied by a -1 because it is is negative so it will change that -x into a x (positive x). You want that postive x. The other important thing to not is that it is a negative ONE, this way nothing changes because anything multiplied by one comes out the same way it started.
4) This step is just something I like to do. I simply put the x on the left side of the equation and the 12 on the right side. It makes no difference to the answer, I just think it looks neater.
Clearly difficulties can be found in step 2 and 3. If you have any questions about this explanation don't be afraid to ask.