Huì (會), néng (能), kě yǐ (可以) and néng gòu (能夠) are common modal verbs in Chinese. Modal verbs are used before verbs, conveying the meaning of possibility, ability, or permission.
Express ability: huì (會) néng (能)/ néng gòu (能夠) kě yǐ (可以)
These four words could be used to indicate someone’s ability to do certain things. When indicating abilities acquired through learning, huì (會) is usually used, which can be understood as “ know how to do something”. Néng (能)/ néng gòu (能夠) and kě yǐ (可以) can be used to express physical ability or capacity to perform some action, convey the sense of "being able to do something". Néng (能) is used more frequently than néng gòu (能夠).
wǒ huì yóu yǒng ,dàn shì wǒ gǎn mào le ,jīn tiān bù néng /bù kě yǐ yóu yǒng.
I can swim, but I am having a cold, so I can’t swim today.
tā yī fèn zhōng néng /néng gòu /kě yǐ zuò qī shí gè fǔ wò chēng.
He can do seventy push-ups a minute.
Huì (會) and néng (能) both can be modified by degree adverbs, indicating that one excels in something or is good at doing something. Huì (會) stresses more on the proficiency, while néng (能) focuses more on the capability.
wǒ mā ma hěn huì zuò fàn.
My mom is good at cooking
tā tè bié néng chī.
He can eat a lot.
Express possibility: huì (會) néng (能)
Huì (會) and néng (能) both could be used to express possibility. Huì (會) indicates the possibility of something happening more or less naturally, which also implies future time. Néng (能) indicates the possibility of someone’s doing something.
míng tiān bú huì xià xuě, dàn huì jiàng wēn.
It may not snow tomorrow, but the weather will cool down.
bú zhī dào tā huì bú huì xǐ huān wǒ wéi tā zhǔn bèi de shēng rì lǐ wù.
I wonder if he will like my birthday present for him.
gōng jiāo chē dōu tíng yùn le, tā hái néng lái ma?
The buses are out of service, will he still be able to come?
Express permission: néng (能) kě yǐ (可以)
Kě yǐ (可以) and néng (能) can be used to express permission to action, and they are interchangeable in questions. Néng (能) is frequently employed in negative sentences that express prohibitions. When it comes to affirmative sentences, kě yǐ (可以) should be used.
wǒ men kě yǐ /néng huí jiā le ma?
Can we go home now?
nǐ cái shí wǔ suì ,bù kě yǐ /néng hē jiǔ.
You're only fifteen, you can't drink.
nǐ yǒu wèn tí kě yǐ /*néng qù wèn lǎo shī.
You can ask the teacher if you have any questions.
Reference : modern mandarin Chinese grammar: A practical guide