Your teacher is wrong.  It's 12p, not -12p.

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Subtract the sum of -3m and -6p from their difference.
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You are to subtract their sum from their difference.

Let's find their sum:

To find the sum write them down in parentheses and put a +
sign between them, like this:

           (-3m) + (-6p)

then simplify that:

             -3m-6p

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Next let's find their difference:

To find the difference write them down in parentheses and put a -
sign between them, like this:

           (-3m) - (-6p)

then simplify that:

             -3m+6p


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Finally we need to subtract the sum FROM the difference.
When you subtract one amount from another, you always start with 
the amount you're subtracting FROM and then you subtract from it.
Since we are subtracting FROM the difference, we write the difference
-3m+6p down first in parentheses, then we write the sum next in 
parentheses, and put a - between them like this:

           (-3m+6p) - (-3m-6p)

Then we simplify:

           -3m + 6p + 3m + 6p

                   12p

So it comes out 12p, not -12p.

Edwin