a) We can synthesize a pentaploid by crossing a hexaploid with a tetraploid. The gamete from the hexaploid will contain 3 chromosomes and the gamete from the tetraploid will contain 2 chromosomes. When these two gametes fuse, a pentaploid is formed.
b) To synthesize a triplet of genotype A/a/a we need to cross A/A organism with a/a/a/a organism. The gamete from the A/A organism will be A and the gamete from the a/a/a/a organism would be a/a. when these two gametes fuse, a triploid of the genotype A/a/a is formed.
c) You have a plant with the genotype A/a. The a* allele has a rare recessive mutation. To obtain a tetraploid with the genotype A/A/a*/a*, we need to expose the cells of this plant to colchicine. This will result in the doubling of the chromosomes and both alleles will be doubled to get the desired genotype.
d) To synthesize a tetraploid of genotype A/a/a/a, we need to cross a hexaploid with a diploid. The hexaploid of genotype a/a/a/a/a/a will give gametes with the genotype of a/a/a. the diploid of genotype A/A will give a gamete with the genotype A. when these two gametes fuse, the tetraploid with the desired genotype is formed.