Can't solve system of linear equations (that need simplification first)
The first mistake I see is here:
$$9x + 6 - 6x - 12 y = x - 3$$ $$9x -6x -x - 12y = -3 +6$$
The second line should read
$$9x-6x-x-12y=-3-6$$
you forgot to invert the sign when moving $6$ to the other side of the $=$ sign.
You were equally sloppy with the second equation, when you did this:
$$5x - 6x + 8y - 15y = 2 - 4$$
We get our second simplified linear equation: $$-x -7y = 2$$
In fact, $2-4$ is not equal to $2$.
The first equation simplifies to $$2x-12y=-9$$ and the second one to $$-7y-x=-2$$