Which one is the correct?
how are you
How do you do?
Why gramatically?
Thanks
They are both correct. “How do you do” is more formal, and “How are you” is informal. You can also say “How are you doing”.
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“How do you do?” is basically limited to introductions. In other words, you can say it only once to someone (just after being introduced) and then never again. Instead of saying “How do you do?” you can also say “It’s nice to meet you” or “Pleased to meet you.”
“How are you?” is a standard greeting. If you see someone daily, you could say “How are you?” to that person every single day.
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I think nowadays almost nobody would say ‘How do you do’ any longer.[YSaerTTEW443543]
TOEIC short conversations: Customer returns cell phone to store because it doesn’t work.[YSaerTTEW443543]
Hi,
I agree with Torsten. ‘How do you do?’ is very formal, very correct and very British.
Alan
[color=white].
Now that’s a fine how-do-you-do.
[color=darkblue]__________________________
[size=92]“If man could be crossed with the cat, it would improve man but deteriorate the cat.” ~ Mark Twain[/size]
Pause the video at 0:26 and you’ll clearly see Kitosdad in the audience, at the bottom left hand corner of your screen. 
Note that the video was filmed inside San Quentin. Now we know the real reason why Kitos hates America so much… 8)
Or very Shakira-ish, in the song of that name. (Her lips don’t hi.)
MrP
hello how do you do?