Correct Answer: She said that she was going home the next day.

Solution : The correct choice is the third option .

Narration Conversion:

• That is used to introduce the reported clause.
• The first-person pronoun (I) is changed to the third-person pronoun (she) .
• The auxiliary verb am is changed to the past tense was , as the simple present tense is changed to the simple past tense.
• Tomorrow is changed to the next day in the reported speech.
• Quotation marks are removed.

Therefore, the sentence in indirect speech is: She said that she was going home the next day.