Choose the option which best expresses the given sentence in indirect…

The correct answer is Option (3) → I asked Bob whether he could complete that work by the next day.

Yes/no question in indirect speech:

Change	Direct	Indirect	Why
Reporting verb	said to	asked ... whether	“Said to” becomes “asked”, and the question is joined with “whether” or “if”.
Tense change	can	could	“Can” moves back to “could”.
Pronoun change	you	he	“You” (Bob) becomes “he”.
Word order	Can you	he could	Subject before verb, “he could”. The question mark becomes a full stop.
Words of nearness	this, tomorrow	that, the next day	“This” becomes “that”, and “tomorrow” becomes “the next day”.
Full sentence	I said to Bob, “Can you complete this work by tomorrow?”	I asked Bob whether he could complete that work by the next day.

Example: She said to me, “Can you drive?” → She asked me whether I could drive.

Why the Other Options are Incorrect?

Option 1: I asked Bob whether he could complete this work by the next day? — Incorrect. "This" is not changed to that, and a reported question ends with a full stop, not a question mark.

Option 2: I asked Bob whether he could complete this work by tomorrow. — Incorrect. "This" and "tomorrow" are left unchanged.

Option 4: I asked Bob whether he could complete that work by the next day? — Incorrect. Everything is changed correctly except the end: a reported question takes a full stop.