This expression is actually pretty easy to simplify. Since all of the actions taking place are either addition or subtraction, we can initiate the first step of removing all the parentheses/brackets from the expression.
m - {n - [p + (m + n - p)]}
simplifies to
m - n - p + m + n - p
Then, we can reorganize the expression so that like terms are next to each other, making it easier to combine the like terms, which will be the next step.
m + m - n + n - p - p
Then, we combine like terms, keeping careful watch over addition and subtaction signs.
2m - 2p
(The n's cancel out because one is negative and the other is positive)
m - {n - [p + (m + n - p)]} simplifies to 2m - 2p.
Hope that helped =)