促进 vs 提倡 vs 推广 vs 宣传 - to promote
促 = to urge; to speed up
进 = to advance
促进 = to promote (something to make it advance).
Example:
(促进)香港旅游业发展 = (to promote/speed up) the development of Hong Kong's tour industry
(促进)血液循环 = (to promote/speed up) blood circulation

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提 = bring up
倡 = support
提倡 = to promote (an idea by voicing support)
Example:
提倡人人戴口罩 = (Promote/ Voice support for)  everyone wearing a mask)
提倡男女平等 = (Promote/ Voice support for) equality between men and women

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推 = push
广 = wide
推广 = to promote (to spread an idea to the public)
Example:
推广男女平等 = (Promote/ Spread the idea of) equality between men and women
推广学习中文 = (Promote/ Spread the idea/ benefit of) learning Chinese

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宣 = to announce
传 = to pass along
宣传 = to promote (to push)
Example:
(宣传)香港旅游业 = (Promote/ Push) Hong Kong's tour industry
(宣传)这个新政策 = (Promote/ Push) this new policy