Difference between 可能 and 能
Literally 能 (néng) talks about capability, whereas 可能 (kěnéng) talks about possibility.

Often 能 is used where "capability" takes on a practical sense (not necessarily about being physically able to do something).  Typically, 可能 is used when deciding if something is a suitable thing to do.

We do the same thing in English: I can swim (capability) vs. I can swim in Summer (possibility).

能 and 不能


  我能游泳。
  Wǒ néng yóuyǒng.
  I am capable of swimming.


This literally implies I am physically capable of swimming.  It doesn't express whether or not I want to go swimming, if I'm allowed to go swimming, and if swimming is a suitable activity (although some of this will be clear from context).

A example where 能 describes a literal capability is:


  罗根不是他的真名,并且还不能游泳。  (source)
  Luōgēn bùshì tā de zhēnmíng, bìngqiě hái bùnéng yóuyǒng.
  Logan is not his real name, and he cannot swim.


An example where 能 describes a practical capability is:


  戴隐形眼镜能游泳吗？  (source)
  Dài yǐnxíng yǎnjìng néng yóuyǒng ma?
  [If someone] wears contact lenses, can they go swimming?


Of course, wearing contact lenses has no effect on one's ability to swim.

可能 and 不可能


  你可能游泳。
  Nǐ kěnéng yóuyǒng.
  You could possibly go swimming.


This indicates the possibility of going swimming; the person we're saying this to may or may not be able to swim.  An actual example is:


  你可能游泳或者骑自行车 (source)
  Nǐ kěnéng yóuyǒng huòzhě qí zìxíngchē
  You could go swimming or ride a bike


Another example is:


  春节期间的水温比较低，我觉得不可能游泳。 (source)
  Chūnjié qíjiān de shuǐwēn bǐjiào dī, wǒ juédé bù kěnéng yóuyǒng
  During Spring Festival, the water temperature is comparatively low, I feel it is not possible to go swimming.


In this example, we could change 不可能游泳 to 不能游泳 to talk about a practical impossibility.



Note: I'm a Chinese learner too.  I tried to ensure this is correct, but please let me know if I've made a mistake I'm unaware of.