알기나해 comes from 알다
it is usually used in a question
when you are upset because someone don't know important thing, you can use it
eg)내 마음 알기나 해?
when you think someone is not interested in it and never know it, you can also use
eg)말해주면 니가 알기나 해?
when someone is going to do something but you want him to do other thing, "-나 해" is used.
eg)청소나 해