Introduction:
Meiosis is a type of cell division that occurs in sexually reproducing organisms. It involves two rounds of cell division, resulting in the formation of four haploid cells from a diploid cell. Haploid cells contain half the number of chromosomes compared to diploid cells.

Given:
- Diploid cell with 2n=12.

Calculating the number of different haploid cells:
In meiosis, there are two rounds of cell division: meiosis I and meiosis II. Each round of division involves specific stages, including prophase, metaphase, anaphase, and telophase.

Meiosis I:
During meiosis I, homologous chromosomes pair up and undergo recombination (crossing over) between non-sister chromatids. However, for the purpose of this question, we are ignoring the effect of crossing over.

- Prophase I: The homologous chromosomes come together and form pairs.
- Metaphase I: The pairs of chromosomes align in the center of the cell.
- Anaphase I: The homologous chromosomes separate and move to opposite poles.
- Telophase I: The cell divides into two daughter cells.

At the end of meiosis I, two haploid cells are formed, each containing half the number of chromosomes (n=6 in this case).

Meiosis II:
During meiosis II, the sister chromatids of each chromosome separate, resulting in the formation of four haploid cells.

- Prophase II: The nuclear envelope breaks down, and the spindle fibers form.
- Metaphase II: The chromosomes align at the center of the cell.
- Anaphase II: The sister chromatids separate and move to opposite poles.
- Telophase II: The cell divides into two daughter cells.

At the end of meiosis II, four haploid cells are formed, each containing the original number of chromosomes (n=6 in this case).

Conclusion:
Ignoring the effect of crossing over, a diploid cell with 2n=12 will give rise to four different haploid cells through meiosis. Therefore, the correct answer is B) 16.

Option d
64.