Final answer:
The correct answer is option 2) Two autosomes and no X chromosome. During meiosis II, sister chromatids have already separated, and if the cell had an X chromosome, it was distributed in meiosis I.
Step-by-step explanation:
A eukaryotic diploid cell in the XX-XO sex determination system with two pairs of autosomes and one X chromosome undergoes meiosis. After meiosis I, the cell divides into two haploid cells with one of each pair of homologous chromosomes, so each cell at this stage has one autosome from each pair and possibly the X chromosome. In meiosis II, the sister chromatids separate, and since the question is about metaphase of meiosis II, each cell will have separated chromatids of the single autosome pairs and possibly a single X chromosome.
Therefore, the correct answer to which combination of chromosomes is possible in one of the two cells at metaphase of meiosis II is:
2) Two autosomes and no X chromosome
This is because by meiosis II, if the cell received the X chromosome, it has already been segregated away into one of the two haploid daughter cells.