Fill in the blank in the following sentence with the most appropriate…

The correct answer is Option (4) → had been sawing

Past perfect continuous (an action in progress before a past event):

• Form: had been + verb-ing (had been sawing).
• Use: for an activity that had been going on for some time up to a moment in the past, when something else happened.
• Deciding clue: "when it started to rain" (simple past) marks the moment that broke into the work.
• This sentence: the woodcutter's sawing was already going on when the rain began, so "had been sawing" fits.
• Complete sentence: The woodcutter had been sawing the log when it started to rain.
  Example: She had been cooking for an hour when the guests arrived.

Why the Other Options are Incorrect?

Option 1: sawed — Incorrect. The simple past shows a single completed action; with "when it started to rain" it would mean that he began sawing after the rain started, not that the work was in progress.
Example: He sawed the plank in half.

Option 2: saws — Incorrect. "Saws" is the simple present, used for habits and general facts; it clashes with the past tense "started".
Example: He saws wood every morning.

Option 3: saw — Incorrect. "Saw" is the base form of the verb "saw" (to cut) or the past tense of "see"; as the past of see, the sentence would say that the woodcutter looked at the log.
Example: I saw a snake in the garden.

Contrast: the simple past "sawed" shows a single finished action; "had been sawing" shows work already in progress when the rain began.