Concept:
- Check each option against both required shifts -- tense and pronoun/possessive -- separately, instead of only building the correct sentence from the rules.
Step 1: Note what needs to shift.
The reporting verb "said" is in the past tense, so the reported clause must generally shift both its tense (present perfect moves back to past perfect) and its pronouns/possessives (first person "I"/"my" must match the third-person subject "she"/"her"). Check each option against both requirements.
Step 2: Test the option that keeps the original pronoun.
"She said that I have completed my assignment on time." Here "I" and "my" are left unchanged, but the speaker is "she," so these must become "she" and "her." This option fails the pronoun shift, so it is rejected.
Step 3: Test the option that keeps the original tense.
"She said that she completed her assignment on time." The pronoun is correctly changed, but the tense stays as simple past "completed" instead of past perfect "had completed." The original present perfect must move one step further back, so this option fails the tense shift and is rejected.
Step 4: Test the option that applies both shifts together.
"She said that she had completed her assignment on time." Both the pronoun/possessive ("I"/"my" to "she"/"her") and the tense (present perfect to past perfect) are shifted correctly together.
Final Answer: She said that she had completed her assignment on time.