Solve for $n$: $|n + 6| = 2 - n$.
To solve for $n$, I need to get rid of the absolute value sign. One way to do that is to consider two cases: either $n + 6 \geq 0$ or $n + 6 < 0$. If $n + 6 \geq 0$, then $|n + 6| = n + 6$ and I can write the equation as $n + 6 = 2 - n$. Adding $n$ to both sides, I get $2n + 6 = 2$. Subtracting $6$ from both sides, I get $2n = -4$. Dividing both sides by $2$, I get $n = -2$. This is one possible value of $n$, but I need to check if it works in the original equation. Plugging in $n = -2$, I get $|-2 + 6| = 2 - (-2)$, which simplifies to $|4| = 4$, which is true. So $n = -2$ is a valid solution. If $n + 6 < 0$, then $|n + 6| = -(n + 6)$ and I can write the equation as $-(n + 6) = 2 - n$. Multiplying both sides by $-1$, I get $n + 6 = n - 2$. Subtracting $n$ from both sides, I get $6 = -2$, which is false. So there is no solution for $n$ in this case. Therefore, the only solution for $n$ is $n = -2$. 