Change the indirect speech to direct speech:
She told him that she was going to visit her hometown the next week.
1
She said to him, “I will visit my hometown next week.”
2
She said to him, “You are going to visit your hometown the next week.”
3
She said to him, “I am going to visit my hometown the next week.”
4
She said to him, “She is going to visit her hometown the next week.”