If the recipe is designed for 4 people than you would need 6 eggs for 8 people (8 is twice as many as 4 so you need twice as many eggs.) similarly, 14 is 3.5 times as many as 4 (14/4=3.5) so you would need 3x3.5=10.5 eggs.
There really isn't any distributing done, as the perimeter is the total length of the shape, and since this is a rectangle it has two two equal sides, 7+7=14 and 13+13=26, 14+26=40 inches