Choose the most appropriate reported construction of the following se…

The correct answer is Option (3) → She asked me if I could answer that question. I replied that I couldn't.

Yes/no question and a short reply in indirect speech:

Other standard changes: do/does → did, will → would, may → might, is/am → was, has/have → had.

Change	Direct	Indirect	Why
Reporting verb	said to ... said	asked ... replied	“Said to” becomes asked for the question. “Said” becomes replied for the answer.
Joining word	“ ” (inverted commas)	if ... that	The question is joined with if (or whether) and statement word order. The answer is joined with that.
Tense change	can	could	The reporting verb is in the past, so “can” becomes could.
Short reply	No	I couldn't	The short reply “No” becomes the full negative “I couldn't”.
Pronoun change	you	I	“You” (the listener, “me”) becomes I.
Words of nearness	this	that	“This” becomes that.
Full sentence	She said to me, “Can you answer this question?” “No”, I said.	She asked me if I could answer that question. I replied that I couldn't.

Example: He said to me, “Can you swim?” → He asked me if I could swim.

Why the Other Options are Incorrect?

Option 1: She asked me if I can answer that question. I said, I couldn't. — Incorrect.

• "can" is not moved back to "could".
• "I said, I couldn't" leaves the reply half in direct speech.

Option 2: She asked me if I could answer that question. I said, I can't. — Incorrect. The reply is left in direct form, and "can't" is not moved back to "couldn't".

Option 4: She asked me if I could answer this question. I replied in affirmation. — Incorrect.

• "this" is not changed to "that".
• "Replied in affirmation" means the answer was yes, but it was "No".

Contrast: in indirect speech "can" moves back to could and the reply is reported with "replied that". "I said, I can't" leaves the reply in direct speech.