Final answer:
Nate will next water and weed the garden on the same day 12 days after April 2nd, which is April 14th. This date is determined by calculating the Least Common Multiple (LCM) of the watering and weeding intervals.
Step-by-step explanation:
The question involves finding a common multiple of two numbers, which is a mathematics problem that is often covered in middle school. Specifically, this problem is about finding the Least Common Multiple (LCM) of 3 and 4, which are the intervals in days that Nate waters and weeds the garden.
Nate waters the garden every 3 days and weeds it every 4 days and he does both on April 2nd. To find out when he will next water and weed on the same day, we need to calculate the LCM of 3 and 4. The LCM of 3 and 4 is 12. This means that every 12 days, both events will align. Since he did both on April 2nd, 12 days later would be April 14th. Therefore, the next date Nate will both water and weed the garden on the same day will be April 14th.