1. Both能 and 可以 could be used to indicate possibility.
e.g.
你能/可以帮我开门吗？(Nǐ néng/kěyǐ bāng wǒ kāimén ma?) Can you open the door for me?
你们能/可以学好中文。(Nǐmen néng/kěyǐ xuéhǎo zhōngwén.) You can learn Chinese well.
2. Both能 and 可以 could be used to indicate permission.
e.g.
我能/可以进来吗？(Wǒ néng/kěyǐ jìnlái ma?) Can I come in?
我们能/可以坐下吗？(Wǒmen néng/kěyǐ zuò xià ma?) Can we sit down?
The negative form 不可以 and 不能 both indicate not permitted.
e.g.
你们不能/不可以走！(Nǐmen bùnéng/bù kěyǐ zǒu!) You can’t go!
你不能/不可以说话。(Nǐ bùnéng/bù kěyǐ shuōhuà.) You can’t talk.
1. 能 is used to indicate someone is good at doing something, the efficiency or the extent to which one does something.
e.g.
哥哥很能吃，每顿吃三碗饭。(Gēge hěn néng chī, měi dùn chī sān wǎn fàn.) My brother can eat a lot and eats three bowls of rice per meal.
妈妈很能睡，每天都睡10个小时。(Māma hěn néng shuì, měitiān dōu shuì 10 gè xiǎoshí.) Mom can sleep a lot, sleeping 10 hours a day.
2. In a rhetorical question, “能不” “能……不……” “能没(有)” are used to indicate possibility.
e.g.
她又赢了，能不开心吗？(Tā yòu yíngle, néng bù kāixīn ma?) She won again. She must be very happy.
他学习了10年汉语，能说得不好吗？(Tā xuéxíle 10 nián hànyǔ, néng shuō dé bù hǎo ma?) He has studied Chinese for 10 years, he must speak Chinese well.
他那么帅，能没有女朋友吗？(Tā nàme shuài, néng méiyǒu nǚ péngyǒu ma?) He is so handsome, he must have a girlfriend.
3. 能 can’t be used as a predicate by itself.
可以 can be used as a predicate by itself to indicate it is not bad or agreement.
e.g.
√ 今天不出门也可以，我们在家看书。(Jīntiān bù chūmén yě kěyǐ, wǒmen zàijiā kànshū.) It’s okay if we don’t go out today, we read at home.
✘ 今天不出门也能，我们在家看书。(Jīntiān bù chūmén yě néng, wǒmen zàijiā kànshū.)
4. The negative form 没能 is used to indicate something is not realized.
e.g.
对不起，我没能帮你。(Duìbùqǐ, wǒ méi néng bāng nǐ.) Sorry, I couldn’t help you.
我没能买到便宜的票。(Wǒ méi néng mǎi dào piányí de piào.) I couldn’t get a cheap ticket.
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