The sentence which uses commas correctly with a non-essential expression is " I spoke to Mr. Smith, my favorite teacher, about my essay" (Option).
Commas are used before and after nonessential words, phrases, and clauses, that is, elements embedded in the sentence that interrupt it without changing the essential meaning.
In this case, commas are employed before and after an apposition, which is the phrase referring to a person already mentioned in the sentence, so that it just adds an unnecesarry information which is not essential.