The sentence in the Direct Speech is in Past Simple Tense. Therefore, the sentence in the Indirect Speech should be in Past Perfect Tense.
Past Simple (Subject + V2 + Object) should be converted into Past Perfect (Subject + had + V3 + Object).
For example:
He said, "Arya sent me a book." (Direct Speech)
He said that Arya had sent him a book. (Indirect Speech)
The following things in the sentence should change when changed from Direct speech to Indirect Speech:
I - he
Bought - had bought
This - that
My - his
Therefore, the correct answer is (c): He said that he had bought that book for his brother.