1. Explain it simply
重新 (chóngxīn) means 'again' or 'anew' - to redo an action from the beginning.
Word order: Subject + 重新 + verb phrase, as in 他重新写了一遍 (he wrote it over again).
重新 always sits before the verb; it cannot go to the end of the sentence or split the verb.
It differs from 再: 再 just adds one more time, while 重新 stresses starting fresh because the first attempt did not work.
2. Show examples
这个句子不对，请重新检查一下。
Zhège jùzi bù duì, qǐng chóngxīn jiǎnchá yīxià.
Sandhi:Zhège jùzi bú duì, qǐng chóngxīn jiǎnchá yíxià.
This sentence isn't right, please check it over again.
重新 sits before the verb 检查
这个方法不好，我们重新考虑一下。
Zhège fāngfǎ bù hǎo, wǒmen chóngxīn kǎolǜ yīxià.
Sandhi:Zhège fāngfǎ bù hǎo, wǒmen chóngxīn kǎolǜ yíxià.
This method isn't good, let's reconsider it.
starting the thinking over from scratch
比赛重新开始了。
Bǐsài chóngxīn kāishǐ le.
The match started over from the beginning.
a fresh restart, not just one more time
3. Share a tip
Keep 重新 in front of the verb - say 重新检查, not 检查重新, and use it when you truly start over, not just add one more time.