About the question: What do you think I should do?

Question

Good day! I just want to ask the difference between "What do you think I SHOULD do?" and "What do you think SHOULD I do?" Thank you very much.  - Tin

 Answer

“What do you think I should do?” is the correct way to ask this question. (You can also use, "What do you think that I should do?" The word that is optional.)

In this question, the dependent clause, “(that) I should do,” is the object of the verb, think. The subject of the dependent clause, I, comes before the verb, should do. They are not inverted to question form. 

Think is one of a large group of verbs that are used in this question construction, which can be described like this:

What do + subject + verb + [that-clause as the direct object of the verb]

Here are some other examples, with the verbs believe, hope, claim, and wish:

• What do you believe (that) John is bringing tonight? [The clause “(that) John is bringing” is the object of believe]
• What do you hope (that) your father is making for dinner? [The clause “(that) your father is making for dinner” is the object of hope]
• What does Jimmy claim we’re supposed to do for homework?
• What does he wish he had said to his teacher? 

As you can see from these examples, these verbs are generally related to thinking and saying.

I hope this helps.