Select the option that expresses the given sentence in direct speech.…

The correct answer is Option (4) → Nandini said, “What a beautiful rangoli my sister has made!”

Changing an exclamation from indirect back into direct speech:

Change	Indirect	Direct	Why
Reporting verb	exclaimed with joy	said	“Exclaimed with joy” tells us Nandini spoke with happy surprise. In her own words this feeling is shown by the exclamation, so “exclaimed” goes back to “said”.
Joining word	that	“ ” (quotation marks)	“That” is dropped. The spoken words go inside quotation marks.
Statement to exclamation	a very beautiful rangoli	“What a beautiful rangoli ...!”	“Very” showed the strong feeling in the report. In the spoken words “What a” + noun and the “!” show it instead, so “very” is dropped.
Pronoun change	her	my	Nandini is the speaker. In her own words “her sister” becomes “my sister”.
Tense change	had made	has made	“Had made” is in the past perfect only because of the past “exclaimed”. The past perfect is formed with had + past participle (V3). Going back, it returns to the present perfect “has made”. The present perfect is formed with has / have + V3.
Full sentence	Nandini exclaimed with joy that her sister had made a very beautiful rangoli.	Nandini said, “What a beautiful rangoli my sister has made!”

With an adjective alone, “very” goes back to “How”. Example: Tara exclaimed that the hall was very crowded. → “How crowded the hall is!” Tara said.

Why the Other Options are Incorrect?

Option 1: Nandini said, “What a beautiful rangoli my sister have made!” — Incorrect. “Have made” does not agree with “my sister”. One person takes “has made”.

Option 2: Nandini said, “What a beautiful rangoli her sister has made!” — Incorrect. The pronoun “her” is not changed. In her own words Nandini says “my sister”.

Option 3: Nandini said, “How a beautiful rangoli my sister has made!” — Incorrect. “How” goes with an adjective alone, as in “How beautiful!”. Before “a” + adjective + noun, the exclamation needs “What”.