Final answer:
An organism with a diploid number of 12 can form 64 different types of gametes, based on the formula 2^n, with n being the haploid number.
Step-by-step explanation:
An organism that has a diploid number of 12 can produce different types of gametes based on the principles of segregation and independent assortment. The number of different possible gamete combinations is determined by the equation 2n, where n is the number of homologous pairs (haploid number). So for an organism with a diploid number of 12, there are 6 pairs of homologous chromosomes.
Applying the formula, we calculate 26 (because the haploid number is half of the diploid number), which equals 64. Therefore, ignoring the potential additional variety from crossing over events, an organism with a diploid number of 12 can produce 64 different types of gametes through the processes of meiosis and random independent assortment of chromosomes.