In Algebra, to undo an operation you perform the opposite operation.

and, remember--whatever you do to one side, you must do to the other side--

Thus you solve your equation--

3=3y-15

3+15=3y-15+15

18=3y

since you want y by itself, you undo the multiplication by 3

divide both sides by 3

so--

18/3=3y/3

6=y

Actually, you need to add fifteen to both sides of the equation in order to remove it from that side of the equal sign.  (Basically, you are doing -15+15=0 on the right side and 0+15=15 on the left.)

When working to try to get a variable by itself, you perform the inverse operation. The 15 is being subtracted from -3y, so the opposite is adding 15 to both sides.

3 +15 = -3y -15 +15

18 =-3y