会 huì (= can, be able to)
能 néng (= can, be able to)

 

会huì refers to a natural (dis-) ability or an acquired skill.

 

能néng refers to a physical (dis-) ability or or an unhampered possibility.

 

Natural Disability

 

他	不	会	去	。
tā	bù	huì	qù	_
he	not	meet	go	_
he, him, other	no, not, after negative question: yes	future: will, meet, be able to	go to, pass away, remove	。
He is not able to go (because he was born without legs).

Listen:

Acquired Skill

 

他	会	说	中	文	。
tā	huì	shuō	zhōng	wén	_
he	meet	say	middle	language	_
he, him, other	future: will, meet, be able to	speak, say	Chinese language, written Chinese language		。
He can speak Chinese.

Listen:

Physical Disability

 

他	不	能	去	。
tā	bù	néng	qù	_
he	not	can	go	_
he, him, other	no, not, after negative question: yes	can, energy	go to, pass away, remove	。
He is not able to go (because of a broken leg).

Listen:

Unhampered Possibility

 

这	儿	他	不	能	工	作	。
zhè	ér	tā	bù	néng	gōng	zuò	_
this	child	he	not	can	work	do	_
here		he, him, other	no, not, after negative question: yes	can, energy	to work, job		。
Here, he cannot work.

Listen: