To maximize the number of carts filled with 4 people, you can start by filling as many carts as possible with 4 people and then see how many people are left.
Each cart can seat up to 4 people, and you have 26 people in total. So, you can fill as many carts as possible with 4 people:
26 / 4 = 6.5
You can fill 6 carts completely with 4 people each. However, you will have 2 people left.
Now, you can't fill another complete cart with those 2 people because each cart can only seat 4. Therefore, you can't completely fill any more carts.
So, the greatest possible number of carts that could be filled with 4 people is 6.