Let's build the indirect version from scratch instead of just checking the four choices, then match it against the options.
Direct sentence: He said, "Where shall I be this time next year?"
Step 1: Since this is a question, the reporting verb "said" must change to a verb that reports a question. Here the speaker is asking about his own future, so "wondered" fits naturally ("asked himself" would also work, but only "wondered" appears among the choices).
Step 2: The question word "where" stays as it is and becomes the connector between the two clauses; no "that" is added and no question mark is used.
Step 3: The clause order changes from question order (shall I be) to statement order (he would be).
Step 4: The modal "shall", used here for simple future with "I", shifts to "would" in reported speech (it would only shift to "should" if the original sentence were asking for advice or a suggestion, which this is not).
Step 5: Time expressions shift away from the speaker's original viewpoint: "this time next year" becomes "that time the following year".
Putting it together: "He wondered where he would be that time the following year", which is exactly option D.
Let's summarize:
This step-by-step build confirms option D is correct.