Choose the sentence that does not have the articles placed correctly :

The correct answer is Option (1) → This is a same pen that I borrowed from you last week.

Same always takes the definite article the, because it points to one particular, identified thing.
Corrected: This is the same pen that I borrowed from you last week.
Example: We studied in the same school.

Why the Other Options are Incorrect?

Option 2: Maya is most likely the person to lead us. — Incorrect. Correct use: the article is right: "the person" refers to one particular person; "most likely" is used here as an adverb phrase and needs no article.

Option 3: I will not be having breakfast today. — Incorrect. Correct use: names of meals (breakfast, lunch, dinner) take no article in general use, so the sentence is correct.

Option 4: Suyesh will be moving to a European city next month. — Incorrect. Correct use: "European" begins with the consonant sound "yu", so "a European city" is correct.