A purple flower with an unknown genotype crosses with a white flower. determine the genotype of the purple flower if purple (P) is dominant and white (p) is recessive

This sounds like a test cross. Because P is dominant, the purple flower could have a genotype of Pp or PP. If all of the offspring of the test cross are purple, then the purple flower has genotype PP. If half of the offspring of the test cross have purple and half have white, then the purple parental flower's genotype is Pp.