Basically all you need to show is –(p-q)=(-p)+q. (1)
Since 0 = (p-q) + (-(p-q)) (additive inverse), we get –p = -q +(-(p-q)). Now substitute for (–p) in (1).
Then m+q-n-p=(m+q)-(n+p) follows. (since -n-p+(n+p) = 0 implies -n-p = -(n+p) (additive inverse))
so technically all u need to show is –(p-q)=(-p)+q. Hope this helps!!