k^2 - 4k - 12 > 0
k^2 - 6k + 2k - 12 > 0
k (k - 6) + 2 (k - 6) > 0
(k - 6) (k + 2) > 0
The product of these factors is greater than 0... That means either both of these are positive or both are negative.
If a * b > 0, then it means either a and b are both positive, or a and b are both negative. That's the only way you can get a product greater than 0.
So EITHER k - 6 > 0 AND k + 2 > 0 (both factors are positive)
k > 6 AND k > -2.
You can write this as a single inequality, k > 6, as any number that is greater than 6 is also greater than -2.
OR k - 6 < 0 AND k + 2 < 0 (both factors are negative)
k < 6 AND k < -2.
You can write this as a single inequality, k < -2, as any number that is less than -2 is also less than 6.
So your solution set is k > 6 OR k < -2.
I hope that helps. :)