The easiest way is to show him the formula for the area of a sphere:
Area = 4 π (radius)²
Thats a good thing to discuss, because its a good thing to remember,
and discussing it will help him remember it.
The important part to look at is the part where it says " (radius)² ".
That tells you that if you multiply the radius by (Anything), then
the area is multiplied by (Anything)².
Since he multiplied the radius by 2, the area was multiplied by (2)² = 4.
Surface area is directly proportional to the square of radius.
Thus, when radius is doubled, Surface area becomes 2² = 4 times.