(n - 2) (n + 4) < 0
If we solved this
(n - 2) ( n + 4) = 0
The solutions would be n = 2 and n = -4
So......the solutions to the inequality lie on the possible intervals
(-inf, - 4) , ( -4, 2) , (2, inf )
Testing n = 0 in the middle interval will make the inequality true, while the outside two intervals don't
So...the solution is (-4, 2) ....and 5 integers lie in this interval