The variables  and  are specifically referring to the allele frequencies of the dominant and the recessive allele in a population, respectively.

Expected genotype frequencies can be seen in the equation:

In this equation, represents the expected genotype frequency of homozygous dominant organisms,  represents the expected frequency of heterozygous organisms, and represents the frequency of homozygous recessive organisms. These values are the expected frequencies in the population, based on the Hardy-Weinberg conditions and allele frequencies; they may not be the values actually observed. To get observed genotype and phenotype frequencies, more information about the size and makeup of the population would be needed.

Hardy Weinberg equilibrium has requirements that must be met by a population in order to confirm that evolution is not taking place:

1. The population must be large in number.

2. There can be no new mutations entering the population.

3. Immigration and emigration cannot change the allelic frequencies of the population.

4. Mating must be random.

5. Natural selection cannot be taking place.

Since it was said that females are selectively choosing which males they mate with, Hardy Weinberg equilibrium is being violated.

Since we know that the population is in Hardy-Weinberg equilibrium and that there are only two alleles, we can use the Hardy-Weinberg equation to solve this problem:

Lets say that  represents the black allele, and  represents the red allele. Since we know that red is recessive to black, only animals with two red alleles will be red. Fortunately, the  portion of the equation is the only portion that deals with red animals (the other two variables are black: both homozygous dominant as well as heterozygous). This means that  is equal to the frequency of red animals in the population: 

Since we now know the frequency of the red allele in the population, we simply subtract it from one in order to find the frequency of the black allele, which turns out to be 0.6.

The two equations pertaining to Hardy-Weinberg equilibrium are:

In this second equation, each term refers to the frequency of a given genotype.  is the homozygous dominant frequency,  is the heterozygous frequency, and  is the homozygous recessive frequency.

From the question, we know that:

We now know the dominant allele frequency. Using the other Hardy-Weinberg equation, we can find the recessive allele frequency:

Returning to our genotype frequency terms, we can use this recessive allele frequency to find the homozygous recessive frequency:

For the Hardy-Weinberg equation to be true, the population in question must be very large. This ensures that coincidental occurrences do not drastically alter allelic frequencies.

Using the Hardy-Weinberg equilibrium equations, you can determine the answer.

The value of  gives us the frequency of the dominant allele, while the value of  gives us the frequency of the recessive allele. The second equation corresponds to genotypes.  is the homozygous dominant frequency,  is the heterozygous frequency, and  is the homozygous recessive frequency.

16% of the population shows the recessive phenotype, and therefore must carry the homozygous recessive genotype. We can use this information to solve for the recessive allele frequency.

We can use the value of  and the first Hardy-Weinberg equation to solve for .

Knowing both  and , you can use the second equation to find the percent of heterozygous organisms in the population.