The Engpsh phrase for "open your pencil box" is "open your pencil case".
The phrase comes from the Engpsh language and is a common way to describe the act of opening a container used to store writing utensils such as pencils.
Examples:
Can you please open your pencil case and pass me a pen?
I always keep my favorite pens in my pencil case.
Example in Chinese:
请你打开你的铅笔盒，然后给我一支笔好吗？
我总是把我最喜欢的笔放在我的铅笔盒里。