Can you please explain this to me?

List all the possible genotypes of a pea plant with purple flowers and round seeds.

When you talk of genotype it refers to the alleles of the organism. Like FFpp, FfPp. For example:

Dominant: White Flower (F)
Recessive: Purple Flower (f)

The possible genotypes for white flowers in the F1 generation are: FF and Ff. When for purple flowers is only ff.
So in the exercise you are proposing, you must list all the possibilities in the alleles for obtaining the physical characteristic of the individuals, take into account if the traits you mention are dominant or recessive.

To determine the possible genotypes of a pea plant with purple flowers and round seeds, we need to understand the genetic principles governing these traits.

Flower color in pea plants is determined by a single gene with two alleles: a dominant allele for purple (P) and a recessive allele for white (p). Seed shape is also determined by a single gene with two alleles: a dominant allele for round (R) and a recessive allele for wrinkled (r).

Since we're looking for a pea plant with purple flowers (PP or Pp) and round seeds (RR or Rr), we can generate a Punnett square to determine all possible combinations of these alleles.

Let's start by writing down the genotypes of the parents:

Parent 1: Purple flowers (Pp) and round seeds (Rr)
Parent 2: Purple flowers (Pp) and round seeds (Rr)

Now, let's cross these parents using a Punnett square:

R r
P PR Pr
p pR pr

By combining the alleles in each parent, we can see that there are four possible genotypes for the offspring in the Punnett square: PR (purple flowers, round seeds), Pr (purple flowers, round seeds), pR (purple flowers, round seeds), and pr (purple flowers, round seeds).

So, the possible genotypes of a pea plant with purple flowers and round seeds are PR, Pr, pR, and pr.