None of that is correct.
Have a look at this
Solve | x^{2} - 4| < 8
I have not done any absolute value quadratic inequalities, here is my attempt. Please check my work, thank you!
|x^{2} - 4| < 8
|x^{2}| +4 < 8
|x^{2}| - 4 < 0
(|x^{2}| -2 ) ( |x^{2}| + 2) < 0
Do we stop here? What do we do next?
(Not sure about this...)
So, a. -x^{2} - 2 < 0 and b. x^{2} -2 < 0 & c. - x^{2} +2 < 0 and d. x^{2} + 2 < 0