This is a past paper of a national test in Thailand. (Manee is a common Thai name and Songla is a province). The answer to this question is (4)How have you been? But I wonder why (3)How do you do? is wrong. I think I can just fill in any greeting so (3) and (4) are both correct.
So is (3)How do you do? okay for this question? and what is the difference between those two?
Because How to you do? is all but dead. But when it is/was used, you only use it for someone you have never met before. And thirdly the proper response to How do you do? is How do you do?
After the greeting Hi, the question How have you been? is natural and actually used.
How do you do?, at least to me (BrE speaker), is a formal phrase for first time meetings only. It may be that some people use it equivalent to How are you doing?, but I would never say that to somebody I knew already, and especially not towards somebody I was familiar enough with to greet with "Hi!".
How have you been?, on the other hand, is a greeting for someone you already know, but haven't seen for a while, and fits much better with the tone of the conversation.
I partly agree. Any greeting would fit in there, so both (3) and (4) are arguably valid answers. But (4) is a BETTER answer, because (3) is essentially an equivalent of "hi". Few Americans, anyway, would say, "Hi. How do you do?" That would be like saying, "Hi. Hello. Greetings." You normally use just one greeting. (4) is a phrase commonly used to follow a greeting. "Hi. How have you been?" or "Hello. How have you been?"
But wow, that's a pretty subtle distinction. I'd limit that to the "advanced colloquial English" class.
