Translation:How many languages can you speak?
For language skills, the verb should be 会 (can, able to). 能 denotes physical capability, like if you are able to attend a conference (and are not thousands of miles away, making it physically impossible) or able to lift a heavy object. Unless, of course, the question is asking about how many languages the person is physically capable of speaking (which would exclude, for instance, an alien language that requires different organs to speak it).
Jumping off of Janus159341's post, "can" can be translated as either 会, 能, or 可以 ... but the connotation of each word is different. I'm not a native Chinese speaker, but as I understand it, 会 is used for knowing how to perform a skill, 能 is used for being physically able to do something, and 可以 is used for having permission to do something. So, for example:
我会开车 means "I can drive" (as in, I know how to drive a car, because I've completed my driving tests, etc.)
我能开车 means "I am able to drive" (as in, I'm not drunk at the moment, so I'm physically capable of driving)
我可以开车 means "I can/may drive" (as in, I have permission to drive)
I think they are treating speaking a language as an ability 能力 so using 能. Speaking a language consists of both knowledge and physical skill. Many Chinese people believe they cannot speak a foreign language because they cannot physically form the words with their mouth. As someone who taught English in China I came across this attitude. This may explain the choice of 能 over 会。