The purpose of Mendel's experiments with dihybrid crosses was to determine whether two traits affect the inheritance of each other. Therefore, the correct answer is D. Mendel wanted to understand how different traits, controlled by separate genes, are inherited and whether they show any relationship or influence each other in the inheritance patterns. This was done by crossing pea plants that differed in two traits, such as seed color and seed texture, and observing the patterns of inheritance in the offspring.