How to use the two pronged approach in this question?

I had a concern regarding the above question. How to approach this question via the two-pronged approach?

I couldn’t understand this. So, any explanation for this will be helpful.

Share your approach.

logic word for the first blank: that (support)
On the left side of “that”, the idea has a negative connotation so the right side will also have negative connotation.

  • As per semantics, the first blank should be something opposite to controversial claims as historians have been debating about them, and schools claim as correct. So, factual claims.
  • the second idea is connected with a logic word or which is support.
  • ii) blank is where extreme strategy should be used where extreme of debate is fully supported or fully rejected.
  • iii) by is supporting logic word so we have double possibility situation here.
  • and I got stuck here

What does “two pronged approach” mean?