You want to know the value of z. You need z alone on the left side. 12 is being added to z. In order to have z alone, you must get rid of the 12 that is being added to z. The opposite operation to addition is subtraction, so you must subtract 12 from the left side to have z alone since 12 - 12 = 0. The rule with equations is that you must do the same operation to both sides of the equation. That means you must subtract 12 from both sides of the equation.
12 + z - 12 = 15 - 12
12 - 12 + z = 3
Since 12 - 12 = 0, you are left with just z on the left side.
