This is an area problem where the area of a circle is pi*r^2.
A quiche with a diameter of 12 has an area of pi*6^2 = 36pi
So if it can feed 6 people, then the serving size per person is 6pi per person.
A quiche with a diameter of 10 inches has an area of pi*5^2 = 25pi
If each person requires 6pi worth of quiche, then 25pi/6pi = 4 1/6 people.
So yes, it can serve 4 people.