To use this method, you have to get it so that one of your variables will cancel when you add the two equations. The best way to do that with these two equations is to make the x in the first equation be -3x. You do that by multiplying it by -3.
So now you have
-3x - 6y = -6
You add that to the other equation and you get
-y = -2 or y = 2.
Then you can just plug that in to the first equation as it originally was and you get
x + 2(2) = 2
x + 4 = 2
x = -2