How does a dihybrid cross give the 9:3:3:1 ratio in the F2 generation?

A dihybrid cross follows two traits at once, for example seed shape (round R dominant, wrinkled r) and colour (yellow Y dominant, green y). Cross two double heterozygotes, RrYy with RrYy. Each parent produces four gamete types, RY, Ry, rY and ry, because the two genes assort independently. Combining these in a 4 by 4 Punnett square gives 16 boxes. Counting the phenotypes: 9 show both dominant traits (round and yellow), 3 show round and green, 3 show wrinkled and yellow, and 1 shows wrinkled and green. That gives the 9:3:3:1 ratio. This works because of Mendel's law of independent assortment, where the inheritance of seed shape does not affect the inheritance of seed colour, so all combinations appear in predictable proportions.