The question is about the changes in the Indian Constitution through the Constitution (86th Amendment) Act, 2002 related to fundamental duties.

Option 1: `To strive towards excellence in individual and collective activity` is one of the fundamental duties, but it was added through the 42nd amendment in 1976, not the 86th amendment in 2002.

Option 2: `To provide opportunities for education to one`s child between the age of 6 and 14 years` is indeed the correct answer. It was added to fundamental duties through the 86th amendment in 2002.

Option 3: `To work for the welfare of women and children` is a part of Directive Principles of State Policy, not a fundamental duty.

Option 4: `To promote peace and harmony` was included in the fundamental duties, but like Option 1, it was added in the 42nd amendment of 1976, not the 86th amendment.

Therefore, the correct answer is option 2 as it is the duty added through the 86th Amendment in 2002.