Question

the absolute value of x+4 is greater than 6 or -6. would it be x is greater than -10 and x is less than 10 or 2?

Answer 1

I am not sure if you have the right question.

The absolute value of any function is greater than zero, so the condition >-6 is superfluous.

Check if the question is not:
x+4 > |6|.

If the question is indeed
|x+4|>6 and |x+4|>-6, just work with the first condition, i.e.

|x+4|>6, which translate to
x+4>6 ....(1) or
-(x+4)>6....(2)

For (1),
x+4>6
x>2
For (2)
-(x+4)>6
-x-4>6
x<-10
So the solution set is:
{x | x<-10 ∪ x>2}
or in interval notation:
(-∞,-10)∪ (2,∞)