It is possible to be capable of doing something but not able to do something.
"capable" is often used with tasks we have the ability/skill/talent to complete.
"able" can have the same meaning but also can be controlled by other factors.
It's best to explain with examples:
I am capable of walking home by myself but I'm not able to because my mum said I need to take a taxi instead.
I am capable of beating you at tennis but I'm not able to beat you today as I'm busy.
I could replace "capable" with "able", but double "able" would make the sentences weirder.