Which Article of the Constitution explains that the executive power of every…

Part XI of the Constitution (Articles 245-263) governs the distribution of power between the Union and the States. Within it, the group of Articles 256-263 deals with administrative relations, giving the Union specific tools to ensure a State's executive machinery does not work against the Union's authority.

Article 257(1) supplies the exact rule the question quotes: the executive power of every State must be exercised so as not to impede or prejudice the executive power of the Union, and the Union's executive power extends to giving a State such directions as the Government of India considers necessary for that purpose.

• Article 261 deals with full faith and credit for public acts, records, and judicial proceedings across States — a recognition provision, not an executive-control provision.

• Article 247 lets Parliament set up additional courts for laws Parliament itself makes — a judicial-administration matter, unconnected to Union-State executive relations.

• Article 123 gives the President ordinance-making power when Parliament is not in session — a legislative emergency power, not an administrative-relations provision.

Since only Article 257 addresses how a State's executive power relates to and can be directed by the Union's executive power, it is the article the question describes.