Check the sentences.

a) What do you think is the best film?

b) What do you think the best film is?

I think both of them are right. Which is more natural for you?

( And what's yours for this year? An optional question:-)
What (do you think) is the best film?
That's incorrect Inch!

Do you know what you are saying?

Which do you think the best film is?

Who do you think you are?

Where do you think you are doing?

These questions are of the same structure.

A -is incorect.
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I think that the sentence
c) Who do you think killed the bambi?
is correct, and sentence a) has the similar structure as c),
which means that the word 'who' in c) is a subject of the sentence as the word 'what' is in a) without concernig the phrase 'do you think'.
Any explanation about it, would you?
When making a selection in a question, use "which," not "what."
Marius HancuWhen making a selection in a question, use "which," not "what."
Hi Marius

Grammarians usually say - and I agree with them - that what is correct when the reference is to a large group:
What is the best film of all time?

Students: We have free audio pronunciation exercises.
Cool Breeze:

You may be right:

BBC NEWS | Talking Point | What is the best film of all time?

Citizen Kane is the best film ever made, according to a poll of movie directors and critics around the world. Do you agree? Tell us which films have had the ...

31 for "What is the best film of all time?"
4 for "Which is the best film of all time?"

But at the New York Times:
"Which is the best" 216 Results
"What is the best" 557 Results
thus I'll stick with which for selections, as what to me is about substance, which is about choice.

This is what one grammarian says:
which and what: the difference

Which and what are often both possible, with little difference in meaning:

Which/what is the hottest city in the world?

is preferred when the speaker has a limited number of choices in mind.

We've got white and brown bread. Which will you have?
(more natural than What will you have?)

When the speaker is not thinking of a limited number of choices, what is used.

What language do they speak in Greenland?
(More natural than Which language ...)
What's your phone number (NOT Which is your phone number?)

Swan, Practical English Usage