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The Hardy- Weinberg equilibrium, model, theory, or rule is also known as the Hardy- Weinberg principle. In the absence of evolutionary effects, the frequencies of alleles and genotypes in a population will, on average, remain constant from generation to generation.

Option (d) is a population that is subjected to natural selection. Natural selection is a natural process in which organisms reproduce under favorable conditions and pass on their characteristics to future generations. With time, organisms adapt to their surroundings and allow this process to take place. As a result, this is a fundamental evolutionary mechanism that aids in the change of heritable features, and these qualities of a population are passed down across generations. It's not in the Hardy-Weinberg equation's population.

$$\begin{gathered} p^2+2pq+q^2=1 \\ {q}^2=\frac{12}{24}=0.5 \\ 2pq=\frac{4}{24}=0.167 \\ {q}^2=\frac{8}{24}=0.333 \\ 0.5+0.167+0.333=1 \end{gathered}$$

Option (a) is a population consisting of $12$homozygous recessive individuals (yy), $8$homozygous dominant individuals (YY), and $4$heterozygous individuals (Yy). It is true that the Hardy- Weinberg equation expresses the frequency of homozygous genotype (AA), homozygous genotype (aa), and heterozygous genotype (Aa), Since all genotypes have a frequency of $1$.

Option (b) is a population in which allele frequencies remain constant throughout time. From one generation to the next, the principle of exposing allele and genotype frequencies in a population will stay constant. For the Hardy-Weinberg equation, this is correct.

Option (c) is the Hardy-Weinberg principle equation.

$p^2+2pq+q^2=1$

where,

$p^2$is frequency for homozygous genotype AA.

$q^2$is frequency for homozygous genotype aa.

$2pq$is frequency for heterozygous genotype Aa.