2X-6Y=12
-2(2X-6Y=12)
4X-10Y=16

Multipy the first equation by -2 so that the X coefficiants only differ in their sign.

-4X+12Y=24
4X-10Y=16
2Y=8
Y=4

Add revised equations and solve for Y.

2X-6(4)=12
2X-24=12
2X=36
X=18

Substitute the value of Y into one of the original equations and solve for X.

(18,4)

Then you get your points.