Here are the sentences filled in with the correct verb forms:

1. Jack asked his sister where she **would go** the following day.
2. The mother told her son **to behave** so impolitely.
3. She asked why Mathew **looked** so embarrassed when he saw Carole.
4. The boy admitted **not having done** the homework.
5. Our grandparents used to suggest **wearing** sunglasses when we were out on bright sunny days.
6. Robert offered **to help** Carlo do the dishes.
7. Tom promised **to give** Janet the answer by the end of the week.
8. John apologized to his mum for **breaking** his promise.
9. Steve warned Mike **not to touch** the wires as it might be deadly.
10. The doctor strongly advised Jasmine **to take** a few days' rest.