First, you need to know what the lines | | mean.
| | around a number means the absolute value.
The inequality is |y|>6
This means that the absolute value of y is greater than 6.
Now, we need to find the absolute value of the choices.
A. y=-7
|-7| is 7
B. y=-1
|-1| is 1
C. y=3
|3| is 3
D. y=9
|9| is 9
Now, we find which of the absolute values work in the inequality.
7 is greater than 6, so that works
1 is less than 6, so it doesn't work.
3 is also less than 6, so that too doesn't work.
9 is greater than 6, so the one will work.
Therefore, choices A and D satisfy the inequality of |y|>6, because |-7|>6, and |9|>6.