增进 zēngjìn to promote

to promote; to enhance; to further; to advance (a cause etc)

How to remember 增进: 增 increase + 进 enter = to promote.

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增进 (zēngjìn) means to enhance or deepen something relational - friendship, mutual understanding, feelings between people.
Fixed collocations: 增进友谊 (zēngjìn yǒuyì, promote friendship), 增进了解 (zēngjìn liǎojiě, deepen mutual understanding), 增进感情 (strengthen feelings/bonds).
Narrower than 增强 (zēngqiáng) - 增进 is essentially reserved for interpersonal or relational nouns, while 增强 covers physical or abstract qualities like strength and confidence.
Formal, common in diplomatic and social contexts (e.g. "promote mutual understanding between peoples").