Which one is correct and why ?
How old do you think Steve is?
How old do you think is Steve?
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How old do you think Steve is?
How old do you think is Steve?
Speech: How old is Steve?
The inversion with think:
How old do you think Steve is?
The inversion in the question is for the verb think, not be.
The car is really very old.
Why do you think the car is very old?
The question concerns another verb and not the statement: the car is very old.
Compare: Is the car very old? That takes the inversion.
If there is a statement about something and you make a question from it using What, How, When, Why etc., it is the verb following those words that become inverted and not the verb in the statement.
They are very rich people. [statement]
Why do you think they are very rich people? [the statement remains the same.] The question is asked with "Why do you think", which is inverted.