Modal verbs
Ability
Can, could, be
  able to, capable of, know
  how to all express ability. 
 Can and be able to
  are similar in meaning. Be able to suggests that
  effort is required.
  -  Chimpanzees can count to 10.
 
  -  Not many people are able to run a marathon.
 
Can has only present and past forms.
  - Can you play the guitar?
 
  - I could swim faster when I was young.
 
Be able to is used for other aspects.
  - Will you be able to play on Saturday?
 
  - He's never been able to finish a novel.
 
  - If you hadn't helped me, I wouldn't have been able to
    pass the exam.
 
Be capable of is often used for things that are
  difficult or unusual.
  -  Kevin is capable of memorizing hundreds of
    phone numbers.
 
  -  I can't believe a child would be capable of
    murder.
 
Know how to means to be able to do something practical
  because you have learned it.
  -  Do you know how to play chess?
 
Could sometimes means 
knew
how to. It refers to a permanent or general ability.
  -  She could read and write by the time she was
    three.
 
Was/were able to
  often combines the idea of ability and achievement.
  -  The car broke down, but we were able to fix
    it.
 
Note that could is not possible
  in this context.
  - The car broke down, but we could fix it.
 
Managed to is similar in meaning to was/were
  able to. It suggests that effort was rewarded by success.
  -  Fortunately, we managed to find a hotel with
    a room.