An ellipse, a circle and a rectangle overlap in the figure. What is the product of the numbers that lie inside both the ellipse and the rectangle?

Inside both the ellipse and the rectangle are 7 (ellipse and rectangle only) and 3 (all three). Product $=7\times 3=21$. 7 forgets the 3 in the centre, 35 multiplies 7 by the 5 that is outside the rectangle, and 63 uses the 9 that is outside the ellipse.