Mendel came up with his law of independent assortment through his investigation studying

All of the answers presented above are correct.
Before Gregor Mendel's research, it was believed that parents' characteristics were passed down to the next generation were not inherited as separate units, but blended together in the next generation.
While he was studying the inheritance of different traits of the pea plant such as the height of the plant, the shape and color of the seed and the variability of the color of the flowers.
During his experiments, he noticed that the simple traits as height were passed down to the filial generation separately, so they were not blending in the next generation as it was previously thought. 
He managed to get purebred plants for certain traits by self-pollination of the pea plants and used them for this experiments.
He determined that some of the traits were expressed more often and with a higher ratio and called them dominant, as opposed to recessive traits that were expressed less often when cross-breeding with an individual with a dominant trait.