Fill in the blank by choosing the suitable option: This is the same b…

The correct answer is Option (2) → that you gave me last week.

Relative pronoun after "the same":

• After the same, the only, all and superlatives, the relative pronoun that is preferred.
• The relative clause must also agree in time with the rest of the sentence: a gift already given takes a past time word such as last week.
• This sentence: "This is the same book that you gave me last week."
  Example: This is the same shop that sold us the faulty fan.

Why the Other Options are Incorrect?

Option 1: what you gave me last week. — Incorrect. "What" means "the thing that" and cannot follow a noun ("book what" is wrong).

Option 3: which you gave me tomorrow. — Incorrect. The past "gave" cannot go with "tomorrow".

Option 4: whom you gave me yesterday. — Incorrect. "Whom" is used only for persons, not for a book.