We can add the two equations together to eliminate $y$:
$(x - y) + (x + y) = 12 + 6$
$2x = 18$
Dividing both sides by 2, we find that $x = 9$.
Substituting this value back into one of the original equations, we can solve for $y$:
$9 + y = 6$
$y = 6 - 9$
$y = -3$
Therefore, the value of $y$ is $\boxed{-3}$.The answer is: -3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Given that $x - y = 12$ and $x + y = 6$, what is the value of $y$?

### Answer:
