It is wonderful to see that you have tried the question. It is also good that you are so neat.
Start answering questions.
Your point is well taken. The short answer is because you have used two minus 1s in the denominator.
Would you agree that 1 = (-1) * (-1)? You should agree.
If that's so then, you could write your factors like this (in the denominator).
1*3(36 - n^2) Notice I put that one in.
Now factor. Keep the one around. It will get used. But do you agree that it does not change anything? 1 times 58 = 58. Nothing has changed about the 58.
So now you factor
1*3*(6 - n)(6 + n)
(-1)(-1) * [6 - n] * (6 + n)
Now you use 1 of the minuses to turn 6 - n around
-1 * (6 - n) = n - 6. You should still have the other one. That's what is missing in what you are trying to do.
So the denominator should be -3(n - 6)(n + 6)
The entire question looks like this when factored.
(n - 6)(n - 6)
==========
-3(n - 6)(n + 6) cancellation will occur
(n - 6)
=====
-3(n + 6)
which is the final answer.