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). |
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. |
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). |
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. |