I don't know what these other people are talking about, this is in fact a system of two equations.
Your first step or two looks correct.
y = x-6
2x - 2(y) = 12
2x - 2(x-6) = 12
Distributing the -2,
2x - 2x + 12 = 12
Combining like-terms,
12 = 12
The x's completely fell out of the equation,
and we end up with a true result.
That means that every x satisfies the system.
The system is called "coincident".
Yes, they are essentially the same line.
That doesn't mean it's not a system though.
If you want to get 0 = 0,
you would subtract 12 from both sides as a final step.
