Question 6011
multiply the first equation by -2 and the second one by 3:
(-2x+3y=6)*(-2) = 4x-6y=-12
(-3x+2y=-6)*(3) = -9x+6y=-18

then add them together:
   4x-6y=-12
+(-9x+6y=-18)
  -5x+0 =-30
divide both sides by -5:
x=6

then plug this back into one of your equations to get the y value:

-2(6)+3y=6
-12+3y=6
3y=18
y=6

The solution is (6,6) check by putting these into the second equation