Explanation:

The diploid number of an organism represents the total number of chromosomes present in its somatic cells, where each chromosome is present in pairs. In this case, the diploid number is 12, which means that there are 12 pairs of chromosomes in the somatic cells of this organism.

Segregation:
During the process of gamete formation, the chromosomes separate or segregate from each other. This means that each gamete will receive only one member of each chromosome pair. In this case, since there are 12 pairs of chromosomes, there will be 12 different chromosomes that can segregate independently into gametes.

Independent Assortment:
Independent assortment refers to the random distribution of different chromosome pairs into gametes during meiosis. This means that the maternal and paternal chromosomes can align in different combinations, resulting in a large number of possible gametes with different combinations of chromosomes.

Calculating the number of different types of gametes:
To calculate the number of different types of gametes that can be formed, we need to consider the principle of independent assortment. Since there are 12 pairs of chromosomes, and each pair can align independently, we can multiply the number of possibilities for each pair to get the total number of different types of gametes.

For each pair of chromosomes, there are 2 possibilities: the maternal chromosome or the paternal chromosome. Since there are 12 pairs, we multiply 2 by itself 12 times to calculate the total number of possibilities.

2^12 = 4096

However, we need to remember that each pair of chromosomes will have identical copies of the same chromosome. Therefore, we divide the total number of possibilities by 2^6 (since there are 6 identical pairs of chromosomes) to get the final number of different types of gametes.

4096 / 2^6 = 64

So, the correct answer is 64 different types of gametes that can be formed based on segregation and independent assortment.