we multiply the equations to make the x variable equal
the first one becomes 3x*2=6x,and the second becomes 2x*3=6x
Then we can subtract and eliminate them
note that the equations do not change if you multiply them by a number,because you can always divide them and again get back you original equation.

6x+4y=2
6x-9y=6
subtract equation [2] from [1],


(6x+4y)-(6x-9y) = 2 - 6
6x+4y-6x+9y=-4
13y=-4
y=-4/13


Now look at eqn [2]
6x-9y=6
6x=6+9y
6x=6+9(-4/13)










x=7/13,y=-4/13

Hope this helps,
Prabhat