I. The adverb 终于(zhōngyú=finally) is used for something is finally happened according to your wish (often after you did some efforts).
I waited him for a very long time. He is finally here.我(wǒ=I)等(děng=to wait)了(le)很(hěn=very)久(jiǔ=long time)，他(tā=he)终于(zhōngyú=finally)来(lái=come)了(le)。
I stood for a half of the day, finally I get an airplane ticket.
我(wǒ=I)站(zhàn=to stand)了(le)半天(bàntiān= a half of the day)，终于(zhōngyú=finally)买到(mǎidào= to buy, have succeed buying)了(le)机票(jīpiào=airplane ticket)。
I worked hard for a very long time, and finally succeeded.
我(wǒ=I)努力(nǔlì=hard-working)了(le)很(hěn=very)久(jiǔ=long time),终于(zhōngyú=finally)成功(chénggōng= to succeed)了(le)。
II. The adverb最后 (zuìhòu=finally) is used for something is finally happened automatically with the result you wish or not.
I (have) waited him for a long time. Finally, he did not come.
我(wǒ=I)等(děng=to wait)了(le)很(hěn=very)久(jiǔ=long time)，他(tā=he)最后(zuìhòu=finally)没(méi=not)来(lái=come)。
I looked at many mobile phones, I finally don’t buy anything.
我(wǒ=I)看(kàn=to look at)了(le) 很(hěn=very)多(duō=many)手机(shǒujī=mobile phone), 最后(zuìhòu=finally)什么(shénme=any)都(dōu=all)不(bù=not)买(mǎi=to buy)。
III. 最后(zuìhòu=last) can be used as an adjective, but 终于(zhōngyú=finally) cannot
The Last Supper is the work of art by Leonardo da Vinci
最后(zuìhòu=last)的(de)晚餐(wǎncān=dinner)是列奥纳多(Liè‘àonàduō=Leonardo)•达(Dá=da)•芬奇(Fēnqí=Vinci)的(de)作品(zuòpǐn=work of art)。
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