If the day before yesterday was Sunday, what day will fall on the day after tomorrow?

Let us establish the timeline from the reference day "Today":
* Day before yesterday = $\text{Sunday}$
* Yesterday = $\text{Sunday}+1\text{ day}=\text{Monday}$
* Today = $\text{Monday}+1\text{ day}=\text{Tuesday}$
* Tomorrow = $\text{Tuesday}+1\text{ day}=\text{Wednesday}$
* Day after tomorrow = $\text{Wednesday}+1\text{ day}=\text{Thursday}$

Hence, the day after tomorrow will be Thursday.