Step 1: Read the diagram:
The female honey bee (queen) has 32 chromosomes, so she is diploid.
Her gametes can develop into a male without fertilisation (arrow C), or join with a male gamete to give a female with 32 chromosomes.
The male is produced from an unfertilised egg, so he is haploid with 16 chromosomes.
Step 2: (a) Cell divisions A and B:
A is meiosis, because the diploid female must halve her chromosome number to make eggs.
B is mitosis, because the male is already haploid, so his sperms are made by ordinary mitosis.
Step 3: (b) Process C:
C is parthenogenesis, the development of an egg into a new individual without fertilisation. This gives the male (drone).
Step 4: (c) Sex determination:
Sex depends on the number of chromosome sets. This is the haplodiploid system: fertilised eggs (diploid) become females, and unfertilised eggs (haploid) become males.
Final Answer:
(a) A = meiosis, B = mitosis. (b) C = parthenogenesis. (c) Haplodiploid sex-determination.