To determine which event comes last in the sequence from the story "Caroline Chases Comets," we can analyze the events provided:
- William builds Caroline a telescope.
- Caroline agrees to be William's assistant.
- William becomes Royal Astronomer.
- Caroline and William build a telescope together.
Since "William becomes Royal Astronomer" signifies a significant achievement and likely occurs after both the construction of the telescope and Caroline's agreement to assist him, it can be inferred that this event is last in the sequence.
Therefore, the correct answer is:
William becomes Royal Astronomer.