Question 482393
This is definitely interesting wording!

Your problem: subtract the sum of -3m and -6p from their difference.


Since the first thing it says is subtract, we know we're going to have to subtract two things.  One of these is "the sum of -3m and -6p".  "Sum" means add, so that means {{{(-3m) + (-6p)}}}, or if you prefer, {{{-3m-6p}}}.  The other thing is their difference, which means subtraction.  The difference of -3m and -6p is {{{(-3m) - (-6p)}}}; recall that a double negative (minus a negative) is the same as a positive, so {{{(-3m) - (-6p)}}} is the same as {{{-3m + 6p}}}.


Now we've dealt with "the sum of -3m and -6p" and "their difference".  Last, we need to subtract the first thing FROM the second thing; that means we need to rearrange those groups.  As an example: if I say "subtract 3 from 5", you'll do 5-3=2, not 3-5=-2.  So we'll rearrange... Instead of the order the question puts it in (sum - difference), we'll flip.  Thus, we'll do difference from above (simplified: {{{-3m+6p}}}) - sum from above (simplified: {{{-3m-6p}}}): {{{(-3m+6p)-(-3m-6p)}}}.  I used parentheses there because we need to distribute the subtraction: {{{-3m+6p+3m+6p}}}.  The -3m and 3m cancel, and {{{6p + 6p = 12p}}}.  Your answer is 12p.


I talked to another math teacher, who agrees that this is 12p, not -12p.  My guess is that your teacher didn't rearrange when subtracting (again, subtracting FROM something means to switch the order).