In order to solve this question,you need to understand what is factorial and how to derive answers to factorial manually, aka without calculator

Firstly, you can use general term formula or just expand per normal to get the expression for coefficient for 3rd term. (I used the former to save space and time)

Secondary, you need to know what (n 2) stands for by looking at your formula sheet. It should be included in the formula sheet for exams and o lvls as well. Replace k with 2, per this question.

Thirdly, understand how factorial works. Basically it works by multiplying all numbers leading up to it. For example, 3! = 3 x 2 x 1.
So, 5!/3! = 5x4x3x2x1 / 3x2x1
Notice that you can cancel the 3x2x1 out cos it appears in the numerator and denominator.
When you have n!/ (n-2)!, you can basically cancel out everything from (n-2) onwards, leaving n x (n-1).

Lastly you can then solve the question.
N should be more than 0, hence -8 is rejected.