The main thing you have to remember is whatever you do to one side of the equation, you must do to the other side to keep the equation true.
-6 - 3y = 27
Add 6 to both sides. The 6 on the left side goes away when you add 6.
-3y = 27 + 6
-3y = 33
Divide both sides by -3. The -3 on the left side goes away when you divide by -3.
y = 33/(-3)
y = -11 Now it is solved for y. :)