3x+2y=6 -6x-3y=-6

One way is to arrange them like this:

 3x + 2y  =  6    --->      multiply this equation x 2           --->   6x + 4y  =  12

-6x - 3y  =  -6   --->      leave this one alone          ---------->  -6x - 3y  =  -6 

Now, if you add down the columns, the x-term will disappear:              y  =  6

Substituting y = 6 into the first equation:    

    3(6) + 2y  =  6      

       18 + 2y  =  6

               2y  =  -12

                 y  =  -2

The idea behind this method:  multiply an equation (or both equations) by a number (or by numbers) so that, when you add down, one of the variables will disappear.