You asked this question:

My answer:

There is no need to be confused. In fact, 'How are you?' is fine for any context, including formal situations.

While there are many other ways of saying this for informal situations, 'How are you?' is the only way to ask about someone's health in a more formal situation. For example, if your boss at work has been unwell, you could ask 'How are you?' and it would be perfectly polite and appropriate.

NB The phrase 'How do you do?' exists, but it does <em>not </em>mean 'How are you?'. It is a rather outdated formula used in formal contexts mean 'I'm pleased to meet you'. Do not try to use it in other situations.

I hope that helps.

"How are you?" This is fine for American English and both formally and commonly used.

"How are you doing?" This is fine for American English and both formally and commonly used.

How is everything? This is also fine in American English and both formally and commonly used, but typically people that use this (between themselves) already know each other. Doctors might be one exception to that.

"How do you do?" This a formal way of asking in British English. However, we don't use it here in the US.

Thanks a lot Su.Ki.

Thank you for correcting my question.

And thanks for the answer. :))

(I hope I didn't make any mistakes)

I don't know how i can ask it by formal way, as a native

Hello. What is so <em>confusing about</em> this?