How could?
怎么可能
Meaning, there is a pre-existing method of resolution.
What are my options?
How can?
怎么会
Meaning, there has not been a developed resolution. What can be we do?
~Joke to help remember the difference between
**May**: A form of could
**Can**: Development of knowledge or skill
Joke:
"Can I go to the bathroom (toilet)?"
I don't know, can you? Do you know how to?
"May I go the bathroom?"
Yes, but not right now, there is not a toilet available.
(knows how to go the bathroom, however the best practice solution is not available).
I am a boy, may I go in the bushes?
(alternate option)
No, you may not. It is bad manners to pee in the bushes in an urban environment.