The Chinese word for to push is
推

tuī

Chinese Definition

push
1. 推

推
1. to push
手推車 - pushcart
推開窗 - to push the windows open
2. to postpone; to delay
推遲 - to postpone
3. (figurative) to put aside; to push away; to dismiss; to explain away
推諉 - to pass the buck
推辭 - to decline with an excuse
推-掉聚會、推-掉採訪、推-掉責任 - to decline a gathering, to decline interviews, to decline responsibility
4. to prompt; to propel
推進 - to propel; to push forward
推波助瀾 - "to drive the billowing waves"; to add fuel to fire
5. to promote; to advertise; to advocate
推廣 - to promote; to popularize
推出 - to present
6. to nominate; to recommend
推薦 - to recommend
推選 - to nominate
唐代詩人首-推李杜。 - Li Bai and Du Fu are ranked the top among the Tang-era poets.
7. to generalize; to broaden
推己及人 - to put oneself in someone's shoes
8. to infer; to deduce
推測 - to estimate; to infer
類推 - to infer by analogy
9. to derive; to reason; to compute
推導 - to derive
推論 - corollary
10. to proceed; to succeed; to form a procession
推移 - to proceed (in time)
11. (Hong Kong, internet slang) to bump a thread in support; to "push".
(syn, yue, push)
(ant, yue, 拉, pull)
12. (ACG or fandom) being a devoted fan of someone; to support someone (in an idol group; etc.)
^前田 @^敦子推 - a person supporting Atsuko Maeda
一生推 - to support someone or a particular group for life
首推 - member that someone like most in an idol group