10. Direct = "Where were you born?" he asked me.
Indirect = He wanted to know where I was born.
As you know we change the tense while converting a direct speech into an indirect speech.
I think the blue part should have been "had been". Because the first sentence or the direct sentence has used
simple past. So for indirect speech we should go one step further back which is past perfect (had been).
Aren't I right?
Is it incorrect if I write "had been born"?
You will see more backshifting from present to past than from past to past perfect, in general.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.