내주다

Meanings

give; offerTo take out and give something kept inside.
give; offer; hand overTo hand over something to someone.
give; yieldTo give one's seat, position, etc., to someone.
give; prepare; grantTo prepare something for someone.

Examples from Lessons (3)

교수님, 시간 을 내주셔서 정말 감사합니다.
Professor, thank you so much for taking the time.
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감사합니다, 시간 내줘서.
Thank you for making time.
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교수님, 바쁘신 와중에 시간 을 내주셔서 감사합니다.
Professor, thank you for taking the time out of your busy schedule to see me.
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Grammar in These Examples

-아/어서Level 2Because of, therefore -(으)시-Level 3Honorific marker -ㅂ/습니다Level 1Formal polite ending