祝你顺利过关 can be translated as "wish you a smooth passage" or "wish you success in passing". This phrase is often used to express good wishes to someone who is facing a challenge or test.
The origin of this phrase is not clear, but it may be derived from the practice of wishing good luck to travelers as they set out on a journey. In Chinese culture, it is common to express good wishes for someone's success or safety when they are embarking on a difficult task.
Here are some examples of this phrase in Engpsh:
I wish you a smooth passage through your exams.
May you have a smooth passage in your new job.
I hope you have a smooth passage in your upcoming surgery.
Here are the corresponding translations in Chinese:
祝你考试顺利。
祝你新工作顺利。
希望你手术顺利。