Which of the following is a personification ?

The correct answer is Option (1) → The carpet talked to me

Personification:

• Personification gives human qualities, actions or feelings to an object, an animal or an idea.
• This sentence: a carpet cannot speak, yet it "talked to me", an act that belongs only to a person. The lifeless object is presented as a companion.
  Example: The old house groaned in the storm.

Why the Other Options are Incorrect?

Option 2: The comet was an island — Incorrect. The comet is called an island directly, without "like" or "as". This is a metaphor; no human quality is given to the comet.
Example: The world is a stage.

Option 3: The big bees bumbled and buzzed busily — Incorrect. The device here is alliteration: the "b" sound repeats in big, bees, bumbled, buzzed, busily. The bees only do what bees do, so no human quality is given to them.
Example: The big brown bear slept in the cave.

Option 4: The wisdom of the old man was like a religious scripture — Incorrect. The old man's wisdom is compared to a scripture using "like", so this is a simile.
Example: His words were like honey to her ears.

Contrast: a non-human thing doing a human action (a carpet talking) is personification; bees that buzz only do what bees do.