Raju said to me that he was going to read a book that week.

The correct answer is: Raju said, “I am going to read a book this week.”

The other options are incorrect because they do not express the same level of certainty as the first option. The second option, “I will be reading a book this week,” is more tentative than the first option. The third option, “I would be reading a book this week,” is even more tentative than the second option. The fourth option, “I may read a book this week,” is the least certain of all the options.

The first option, “I am going to read a book this week,” expresses the highest level of certainty. This is because it uses the present progressive tense, which is used to talk about things that are happening or will happen in the near future. The other options use the simple present tense, which is used to talk about things that are true in general or that happen regularly.

In this case, Raju is saying that he is going to read a book this week. This means that he has already decided to read a book and that he is planning to do it in the near future. The other options do not express this level of certainty.