'How do you do', doesn't mean the same as 'How are you?' It is the formal response used between two strangers when they are first introduced. It is only used in very formal situations and the meaning is nearer to, 'Nice to meet you.' These days people don't say, 'How do you do' very often. As it is such a formal expression, the correct response is to reply with the same and to reply with, 'How do you do'. 'How are you?' is used with people who know each other and the responses Mister Wright suggested can all be used.

- How do you do? :used as a greeting after you have been introduced to a stranger (formal greeting). This expression is becoming old-fashioned (passing out of current use). The usual reply (or the correct response) is also "How do you do?". So it's not correct to say "Great, thank you. And you?" here. (You can use it in an informal greeting to a friend). You can use "It's a pleasure to meet you." or "Pleased to meet you." instead of "How do you do?". - How are you? (informal) = How are you doing? (very informal) Used informally to ask how a friend is, and how life is going. These responses are generally expected: Very well, thank you. And you? (formal) Fine / Great / All right / Good... (informal) :)

No, it is not a mistake. You can reply with: "Fine, thank you. And you?" "Great, thank you. And you?" "Good, thank you. And you?" (If the question is "how are you?" Many people think this is incorrect, but it's not). "I'm well, thank you". (Used more if you have been sick or injured, an someone inquires about your health).

yes ! i think its ok! because i use this!

there's nothing wrong about the response "Great, thank you, and you?" only that this is only a casual response used mostly in a casual talk. the more formal response would be "I'm doin' great, thank you, and you?" :)