Which region has a greater area?

Let the radius of the big circle be $2r$ ,

∴ Radius of each of the smaller circles = $\frac{2r}{2} = r$ ,

∴ Area (yellow) can be written as:

$A = π (2r)^2 - 4 π(r)^2$ (Area of the four smaller circles) + Green Area (since, Green Area has been counted twice in the previous subtraction)

$\implies$ Yellow Area = $4πr^2 - 4πr^2 +$ Green Area.

$\implies$ The yellow area = The green area.

I like Hana's solution much better than mine.

I rotated two of the smaller circles 90 degrees overlaying them completely on the other two circles. This remains consistent with the requirements of the puzzle as defined.

Set the radius of a small circle as r, and thus, the radius of the large circle is 2r.

Therefore, the area of the larger circle is (pi)(2r)^2 = 4(pi)r^2

The green area (the area of the two remaining smaller circles) = 2(pi)r^2

The yellow area = the area of the large circle - green area: 4(pi)r^2 - 2(pi)r^2 = 2(pi)r^2