Step 1: Read the quoted text.
The clause promises free and compulsory education for all children up to fourteen years within ten years of the Constitution's commencement.
Step 2: Locate the part of the Constitution.
This is a Directive Principle from Part IV, dealing with education.
Step 3: Recall the original Article 45.
Article 45 originally carried exactly this directive on free and compulsory education up to age fourteen.
Step 4: Note the later change.
The 86th Amendment (2002) created Article 21A as a fundamental right and recast Article 45 for early childhood care, but the quoted wording is the original Article 45.
Step 5: Eliminate the others.
Article 41 covers right to work and assistance, Article 42 maternity relief, and Article 46 welfare of weaker sections, none matching the quote.
Step 6: State the answer.
The Article is 45, option D.
\[ \boxed{\text{Article 45}} \]