*"채"가 무슨 뜻인지 몰라요. (or more naturally, 모르겠어요.)
Here, it means "with" but because there's "않은" in front of it, it becomes "without"
(When you give flowers to Germans, it's better to keep them in odd numbers and WITHOUT too much packaging.")
Other example:
손으로 턱을 괸 채 나를 쳐다보고 있었다.
(He was looking at me WITH his chin propped on his hands.)
Hope that helped!
The sentence though might be a bit too complicated at your stage right now.
I recommend you study simpler sentences that are shorter and with just basic grammar.
When you feel comfortable with those and you're not making a lot of mistakes when you make your own sentences, then you can move up a level from there. :)