Change the narration: "Shall I ever go there again?" he asked.

He asked when he will go there again.

He asked when he would go again there.

He asked whether he would go there again.

None of these

Direct Speech: "Shall I ever go there again?" he asked.

Indirect Speech: The question is yes/no type, so it changes using "whether" or "if".

"Shall I" becomes "he would" (future in past).

Pronoun "I" → "he"

Hence, the correct transformation is:

He asked whether he would go there again.