|"How do you do?"
"How are you?"
If I had a Euro for every time someone got this one wrong - I'd be a rich bunny!
How do you do?
This is not a question. It is another, very formal way of saying "Hello." It is also very British.
The correct response is; "Pleased to meet you." or "How do you do." or just "Hello."
We only really use it the first time we meet someone.
How are you?
This is a question, but the person asking it doesn't really want to know the truth about your aching back or hangover.
A polite response is; "I'm fine thanks. And you?"