The correct answer for this question is option 2, which is article 40 of the Indian Constitution. Article 40 directs the state to organize village panchayats and endow them with necessary powers and authority to function as self-governing units. It aims to promote grassroots democracy and ensure the participation of villagers in decision-making processes.

Option 1, article 32, is incorrect as it pertains to the Right to Constitutional Remedies. Option 3, article 45, is incorrect as it pertains to the provision of free and compulsory education for children. Option 4, article 51, is incorrect as it pertains to the promotion of international peace and security.

Therefore, the correct article that introduced the Panchayat Raj system in India is article 40.