Complete the following sentence using the most appropriate word from…

The correct answer is Option (2) → by

The preposition "by" meaning "according to":

• By can mean according to or judging from, especially with a clock, watch or rule.
• "What is the time by your watch?" asks what time your watch shows.
• Complete sentence: What is the time by your watch?
  Example: It is half past six by my watch.

Why the Other Options are Incorrect?

Option 1: in — Incorrect. In shows position inside something or a period of time; "the time in your watch" would mean something inside the watch.
Example: The keys are in the top drawer.

Option 3: within — Incorrect. Within means inside a limit of time, place or amount; it does not mean "according to".
Example: Please finish the work within an hour.

Option 4: about — Incorrect. About means concerning or approximately; "the time about your watch" is not English.
Example: We talked about the examination.