The two ways of relating what a person has said are 1)direct and 2)indirect (reported).
In the direct speech, the exact words of the original speaker are repeated.
In the indirect speech (reported speech), the exact meaning of what the speaker told is expressed but not necessarily in the speaker’s exact words.
Option A is correct as the conjunction if is used and 'can' is transformed to 'could'.
Options B, C, and D are wrong as 'can' cannot be used, 'if' is not used, and 'could' is not used respectively.
The correct answer is A) He asked me if I could solve that problem.