Example sentences
tā他kě可néng能bù不lái来le了。
He probably won't come.
zhè这bù不kě可néng能。
That's impossible.
About this word
可 means may, 能 means to be able, and doubling two possibility words gives possible. Chinese uses 可能 as an adverb (他可能不来, he might not come) and as a noun (有这种可能, that is possible). The sense is real possibility rather than permission, so it is not interchangeable with 可以, which grants permission, or with 能 and 会, which cover ability and learned skill. Position is before the verb, and 很可能 (quite possibly) is a common hedge in speech, while 不可能 is the flat denial.
The story behind the character
可
可 is 口, a mouth, with 丂 at the side giving the sound. Xu Shen wrote 可, 肯也: to be willing, to say yes. A mouth making the sound 丂, and the meaning landed on approval. Can, may and okay all grew out of a yes. 可以 puts 可 with 以, to use, so the phrase reads as yes, let us use this.
能
能 was originally a bear. The earliest form is a bear: fat body, short legs, ears perked up. Xu Shen wrote 能, 熊属: "of the bear family." Then it was borrowed to mean "able to," and the bear lost its character. So people stuck four fire-dots on the bottom to make the new 熊. When you say "I can do it," you're literally saying "I bear."