Correct option is B
Article 21 of the Indian Constitution provides that no person shall be deprived of his life or personal liberty except according to the procedure established by law. This article has been broadly interpreted by the Supreme Court of India to include various rights that are essential for the full development of one's personality. Among the options given, the Right to Livelihood, Right to Free Education up to the age of 14 years (not 16 as mentioned, which is a misinterpretation; however, education is considered under Article 21A for children aged 6 to 14 years), and Right to Reputation are directly interpreted under the ambit of Article 21 through various landmark judgements. The Right against public Hanging and Right to Sustainable Development are not explicitly mentioned under Article 21 but are derived from the broader interpretation of the right to life and personal liberty.