Here's the context:
A: Let me explain what's wrong with this long sentence.
B: No, thanks. Just show me the place where you see the mistake and I'll try to find out on my own what is wrong with it.
The question is, whether in the second part of the sentence (B's reply) the anticipatory "it" after "to find out" is needed:
"... I'll try to find it out on my own what's wrong..."
In my opinion the "on my own" phrase calls for it, whereas without it, there's no need for "it":
I'll try to find out what is wrong with it.