Choosing the most appropriate answer from the given list, convert the…

The correct answer is Option (2) → "Did Bill give you that ring?", I asked Sara.

Indirect to direct speech (a yes/no question):

Change	Indirect	Direct	Why
Connective	whether	“ ...?”	“Whether” is removed. The question is put in inverted commas and ends with a question mark.
Word order	Bill had given	Did Bill give ...?	A direct question uses the question order with did: “Did Bill give ...?”
Tense change	had given	did ... give	The past perfect “had given” goes back to the simple past “did ... give”.
Pronoun change	her	you	“Her” (Sara) becomes “you”, since the speaker now addresses Sara.
Full sentence	I asked Sara whether Bill had given her that ring.	“Did Bill give you that ring?”, I asked Sara.

"Asked" stays: "I asked Sara".

"That ring" stays.

Example: He asked me whether I had seen the film. → He said to me, “Did you see the film?”

Why the Other Options are Incorrect?

Option 1: "Did Bill willing to give that ring?, "I asked Sara. — Incorrect. "Did Bill willing" is ungrammatical (did needs a base verb), the idea of willingness is added, and "you" is missing.

Option 3: "Can Bill give you a ring?", I asked Sara. — Incorrect. "Can" asks about possibility in the future, and "a ring" loses the particular ring. The question was whether he had given it.

Option 4: "Should Bill give you rings?", I asked Sara. — Incorrect. "Should" asks for advice, and "rings" is plural. Both change the meaning.