Solution;
The answers to this question contain many verb -ing modifiers, also know as participial phrases. When a participial phrase follows a clause, and is separated from that clause by a comma, the phrase modifies or extends the entire clause and is associated with the subject and verb of the clause.
(A) Castro, masterminding the creation of the Cohiba cigar brand, quit smoking for health reasons, at age 59
The presence and placement of the participial phrase, "masterminding the creation of the Cohiba cigar brand," results in the sentence's seeming to convey that masterminding the Cohiba cigar brand and quitting smoking are somehow related, as if in quitting smoking were part of or the result of masterminding the cigar brand. That meaning is not logical.
Further, "quit smoking for health reasons" is somewhat ambiguous, possibly conveying that Castro was smoking for health reasons.
(B) Castro, masterminding the creation of the Cohiba cigar brand and, at age 59, quitting smoking for health reasons
This version has no main verb.
(C) Castro, who masterminded the creation of the Cohiba cigar brand, quit smoking, at age 59, for health reasons
This version clearly conveys one main point, that Castro "quit smoking". The non restrictive modifier "who masterminded the creation of the Cohiba cigar brand", simply adds information to the sentence.
(D) Castro, who, having masterminded the creation of the Cohiba cigar brand, quit smoking, at age 59, for health reasons
This version has no main verb.
(E) Castro masterminded the creation of the Cohiba cigar brand, quitting smoking, at age 59, for health reasons
In this version, the participial phrase, "quitting smoking, at age 59, for health reasons" is placed so as to modify the entire preceding clause, The conveyed meaning is therefore that by, in the process of, or as a result of masterminding the creation of the cigar brand, Castro quit smoking. That meaning is illogical.
The correct answer is C.