To earnestly implore a good official or respected person to stay; to try to retain someone by strongly pleading with them (literally, 'to pull the cart shaft and lie in the ruts').
这位老师深受学生爱戴，毕业时大家纷纷攀辕卧辙，希望他能多留几年。
This teacher was deeply loved by the students, and when they graduated, everyone earnestly pleaded, hoping he could stay for a few more years.
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