Translation:The teacher can speak many languages.
Oops, the usage of these modal verbs are actually much more complex than it looks.
能 = can, in regard to ability, status and permission (if there is any).
will, a wish or a future event.
know how, in regard to the mental ability of a living thing. For animals, physical abilities like running, flying can also use this in a figurative way.
(derivation from 2) be good at.
One should note that both item 1 and 2 may apply when the subject to be a living being. So there is a possibility for ambiguity. But it's not hard to judge when a context is given. If the sentence describes an abstract behavior, it means "know how". If it is an event, it means "will".
- Usage of "can":
孔雀能飞吗/孔雀会飞吗？Can a peacock fly?
孔雀能活多少年？How many years can a peacock live? (It's not "learnable".)
这只孔雀会飞吗？Can this peacock fly? (Or is it too young?)
这只孔雀能飞吗？Can this peacock fly? (Or is it too young, hurt or caged?)
我能说汉语/我会说汉语。I can speak Chinese.
这架飞机能飞吗？Can this plane fly? (A plane is not a living thing)
我会做饭，但现在不能做。I know how to cook, but I can't. (I don't have time or kitchen wares.)
我能用这台机器，但不会用。I can use this machine, but I don't know how to use it.
- Context, abstract behavior:
我能做饭。I can cook. (I learned it, or I have the tool, or I'm not tired.)
我会做饭。I know how to cook. (I learned it.)
- Context, event:
我明天能来。I can come tomorrow. (It's sunny tomorrow.)
我明天会来。I will come tomorrow. (I promise.)