We are given that n is a number which lies between m and -m.

Since m is greater than -m, we know that n is greater than -m and less than m. Therefore, we can say that:

-m < n < m
Now, let's consider each statement:

n - m > 0: This statement may or may not be true, depending on the value of n and m. If n is greater than m, then n - m is positive. But if n is less than m, then n - m is negative.

m + n > 0: This statement is always true, since we know that -m < n < m. Adding m to both sides of the inequality gives:

m - m < n + m < m + m

0 < m + n < 2m

Since m and n are both less than m, their sum must be positive.

n > 0: This statement may or may not be true, depending on the value of n. If n is positive, then this statement is true. But if n is negative, then this statement is false.

|n| > 0: This statement is always true, since the absolute value of any number is always greater than or equal to 0.

m > 0: This statement may or may not be true, depending on the value of m. If m is positive, then this statement is true. But if m is negative, then this statement is false.

|m| > 0: This statement is always true, since the absolute value of any non-zero number is always greater than 0.

Therefore, the statements that must be true are:

m + n > 0
|n| > 0
|m| > 0
Answer: (B), (D), (F)