AP Biology Mendellian Genetics Question - What are the genotypes of the parents? The phenotypes?

Since the two possible outcomes are purple and yellow eyes, and since more have purple eyes the genotype would probably be Pp for both parents so:
a) Pp and Pp
b)the parents have purple eyes
c) either PP, Pp or pp

Punnett squares just show the possible outcomes.
another possible genotype is pp and Pp tho

the punnett square is a model designed to show you the proable types of offspring from the mating of the parents. If you know the genotypes of those parents then you can predict the types of traits that the offspring will have----whether there is one child or ten, the probability of their genotypes will fall into the pattern of the punnet square you have configured---so......
a) in order to have offspring with both alleles expressed, each of the parents must have both alleles---the parents are heterozygous for eye colour--they are Pp (dad) and Pp (mom)
b) the phenotypic expression of heterozygous alleles would be the dominant trait---so they are both purple eyed
c) if you analyze the offspring ratio of  4 purple to 2 yellow--and reduce it to 2:1, it then is close to the Mendelian ratio of 3:1 for the single trait inheritance (but it's a small sample(6) of offspring compared to the hundreds and thousands of seeds that Mendel worked with) the Purple genotype offspring could be PP or Pp and the yellow eyes would be pp

Well think about all the possibilities mathematically, and you can see that the two parents have the genotype Pp. Since four out of the six children have purple eyes, then that means that this particular couple had a 67% chance of having a phenotype conveying the dominant gene and 33% chance of the children having the recessive gene. To solve this, compare the different percents you would get with every combination of parents using a conventional punnet square.

PP and PP parents:
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100% chance purple eyes; 0% chance yellow eyes

PP and Pp parents:
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100% chance purple eyes,0% chance yellow eyes.
 There is a 50% chance genotype is PP and 50% chance the genotype is Pp. However, because "P" is dominant, it masks the recessive "p", thereby resulting in a purple-eyes offspring every time.

PP and pp parents:
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100% chance purple eyes, 0% chance yellow eyes.
There is a 100% chance the genotype is Pp, but the dominant "P" present in every genotype produces a phenotype of purple eyes in every offspring.

Pp and Pp parents:
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75% chance that there are purple eyes, and 25% chance yellow eyes
The genotypes in this combo would be 25% PP, 50% Pp and 25% pp. Now both PP and Pp would produce a phenotype of purple eyes because they all have at least one dominant gene "P", thereby having a 75% chance of having purple eye-ed offspring. The genotype pp does not have the dominant "P", so the offspring would have 25% chance of being yellow eyed.

pp and pp parents:
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100% chance yellow-eyes and 0% chance purple eyes.
There is no dominant gene present, so all the offspring would have yellow eyes.

Based on all of these combinations, every combo would give you the extremity of either 100% purple or 100% yellow eyes (in the phenotype, not the genotype, and you ARE focusing on only the phenotype) except for the Pp an Pp combo, which gives you a moderate ratio of 3:1 purple to yellow. Since the couple had both yellow-eyed and purple-eyed offspring, this is the only combination that gives you similar results.