Males typically have one X chromosome and one Y chromosome in each body cell with a total of 46 chromosomes 46 XY. If 6 is the haploid number then the organism will have 2x6 chromosomes six pairs. Crossovers farther randomly mix up the alleles that each gametes would.
223 8388608 different combinations.
Now 1 gamete from mother and one from father contribute in formation of zygote and thence an offspring. Hence the different possible chromosome combinations can be of the following. Crossovers farther randomly mix up the alleles that each gametes would. However this includes each handshake twice 1 with 2 2 with 1 1 with 3 3 with 1 2 with 3 and 3 with 2 and since the orginal question wants to know how many different handshakes are possible we must divide by 2 to get the correct answer.