I think I see your difficulty with this problem. Whichever technique you try you arrive at an equation that makes no sense. The reason is that there are no numbers x and y that satisfy the equations.
The first equation says that
2x - 3y = 12
Now look at the left side of the second equation. There is a common factor of -2, thus the left side of the second equation is
-4x + 6y = -2(2x - 3y)
If x and y satisfy the first equation then 2x - 3y = 12 but then the left side of the second equation is
-2(2x - 3y) = -2(12) = -24
But if x and y satisfy the second equation this value must be 15. Hence if x and y satisfy the first equation they can't satisfy the second and thus the system of equations has no solution.