The correct option for the given statement is Option 3: Article 21 and freedom guaranteed in part III of the Indian Constitution.

Article 21 of the Indian Constitution guarantees the right to life and personal liberty to every individual. The Supreme Court of India has interpreted this article to include the right to privacy as an intrinsic part of the right to life and personal liberty. This interpretation was first given in the landmark judgment of K.S. Puttaswamy v. Union of India, in which the Supreme Court declared that the right to privacy is a fundamental right under the Indian Constitution.

Part III of the Indian Constitution contains a list of fundamental rights that are guaranteed to all citizens of India. These rights are enforceable by the courts and are considered essential for the protection of individual liberty and dignity. These fundamental rights include, among others, the right to equality before the law (Article 14), the right against discrimination (Article 15), and the right to freedom of speech and expression (Article 19). The provisions in Part III of the Constitution protect various aspects of an individual`s life and liberty, including the right to privacy.

The other options provided in the question are not correct or complete.

Option 1 mentions Article 14, which guarantees the right to equality before the law, but does not directly relate to the right to privacy. The provisions under the 42nd Amendment to the Constitution deal with the duties and responsibilities of citizens and do not relate to the right to privacy.

Option 2 mentions Article 17, which prohibits untouchability, and the Directive Principles of State Policy in Part IV of the Constitution. While the Directive Principles of State Policy include provisions related to privacy and personal liberty, they are not enforceable by the courts and are only guiding principles for the government.

Option 4 mentions Article 24, which prohibits the employment of children in hazardous industries, but does not relate to the right to privacy. The provisions under the 44th Amendment to the Constitution deal with the election of the President and Vice President of India and do not relate to the right to privacy.

In conclusion, the correct option that implies the statement "Right to Privacy is protected as an intrinsic part of Right to Life and Personal Liberty" is Option 3: Article 21 and freedom guaranteed in Part III of the Indian Constitution.