Final answer:
In megasporogenesis, the megasporocyte divides meiotically to produce haploid megaspores, of which one survives and eventually gives rise to the female gametophyte through mitosis.
Step-by-step explanation:
In the process of megasporogenesis, the megasporocyte (also known as the megaspore mother cell) divides meiotically to produce four haploid megaspores. However, typically only one of these survives and is larger than the others.
This single surviving haploid megaspore then undergoes mitotic divisions during the phase known as megagametogenesis, leading to the formation of the mature female gametophyte or embryo sac, which contains an egg cell among other cellular components necessary for fertilization and development of the seed. Therefore, the correct answer to the question is 'b. megasporocyte; meiotically'.