Tricky!!!
First notice that we can perform some factoring in parts
We'll start by rearranging the terms to get some like terms together.

Take: $mx + qy − nx − py = 0$
Rearrange to get: $mx − nx + qy − py = 0$
Factor in parts to get: $x(m − n) + y(q - p) = 0$
Now subtract $y(q - p)$ from both sides to get: $x(m − n) = -y(q - p)$
Rewrite the right side of the equation as follows: $x(m − n) = y(-q + p)$
Simplify to get: $x(m − n) = y(p - q)$

Divide both sides by $x$ to get: $m − n = \frac{y(p - q)}{x}$

Rewrite the right side of the equation to get: $m − n = \frac{y}{x}(p - q)$

Replace $p − q$, and $\frac{y}{x}$ to get: $m − n = -\frac{1}{3}(2)$

Simplify to get: $m − n = -\frac{2}{3}$

Multiply both sides by $-1$ to get: $-m + n = \frac{2}{3}$

Finally, rewrite as follows: $n - m = \frac{2}{3}$

Answer: A

Cheers,
Brent