The idiom "out of the woods" means out of danger.
The other options are incorrect.
- "To lose contact" is not the same as out of the woods. Losing contact means to stop communicating with someone.
- "To meet with disaster" is not the same as out of the woods. Meeting with disaster means to experience something bad or unfortunate.
- "Not adhering to rules" is not the same as out of the woods. Not adhering to rules means to break the rules.
The idiom "out of the woods" comes from the idea of being lost in a forest. When someone is lost in a forest, they are in danger of getting hurt or even killed. However, if they can find their way out of the woods, they are safe. | 
