Initially by meiosis and then by mitosis.
This question is confusing. What I can tell you though, is that mitosis is the process in which cells divide and cause the animal fetus to grow, but it is meiosis that ensures the animal can develop as a fetus initially. (The 4 resulting haploid cells form a sperm gamete and an egg gamete, and they come together to form a zygote, which eventually develops into a fetus)
