能 (néng) is another Chinese word that is often translated as "can." However, it has a slightly different meaning than the others. 能 is used to express ability or possibility of doing something. This article will further explain its use.
Structure
Expressing Ability
The verb 能 is used to express either ability or possibility.
Examples
能 indicates ability when used with activities that are not consciously learned or studied.
我 能 吃 四十 个 饺子。
Expressing Possibility
Examples
When used with activities that are consciously learned or studied, 能 generally means that circumstances do not allow execution of the action. In other words, it's not possible. Sometimes this is a bit of an exaggeration and actually just means it's "not allowed."
上课 的 时候 不 能 说 英文。
Other usages
From these examples we can see such circumstances might be pertaining to getting someone's consent or reliant on the speaker's health. 会 can be used instead if the speaker wishes to express that they are able to execute an action requiring a consciously studied skill.
Because 能 can express possibility, it is often used to form polite questions, something like "would it be possible" in English:
你 能 不 能 给 我 那 本书?