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The word 献殷勤 is formed by combining the verb 献, meaning "to offer", with the compound term 殷勤, meaning "ardent diligence" or "warm attentiveness". This creates a verbal phrase where 献 acts upon 殷勤, literally "to offer ardent diligence", which idiomatically conveys showing excessive attentiveness or currying favor.

Word Definition - 献殷勤

xiàn yīn qín to be particularly attentive to (an attractive young lady or man etc); to fawn upon (an influential politician etc); to court sb's favor; to ingratiate oneself