If the inequality has the same number on both sides for the answer is that ok?

If the problem was |6y+6| < 0, then you would be able to say 0 < 6y+6 < 0 (because of the template below)

Template:
if |x| < k, then -k < x < k



However, the inequality sign is not a "less than" sign. Instead its a "greater than" sign. 

So instead you should use this template

if |x| > k then x > k or x < -k

So if 
|6y+6| > 0
then
6y+6 > 0 or 6y+6 < 0

Solve each inequality for y
6y+6 > 0
6y+6-6 > 0-6 ... subtract 6 from both sides
6y > -6
6y/6 > -6/6 ... divide both sides by 6
y > -1

Do the same for the other inequality
6y+6 < 0
6y+6-6 < -6
6y < -6
6y/6 < -6/6
y < -1



So overall, the two solutions are y > -1 or y < -1

The keyword "or" is important. You can only choose one inequality or the other, but not both.