What produces egg and sperm cells during the life
cycle of a plant?

The gametophytes produce gametes (eggs and sperm). Fusion of gametes (fertilization) produces a zygote. The zygote grows into the next generation of sporophyte.

During meiosis, a diploid parent cell, which has two copies of each chromosome, undergoes one round of DNA replication followed by two separate cycles of nuclear division to produce four haploid cells. These cells develop into sperm or ova.

The plant starts life as a seed, which germinates and grows into a plant. The mature plant produces flowers, which are fertilised and produce seeds in a fruit or seedpod. The plant eventually dies, leaving seeds which germinate to produce new plants.

a unit of heredity that is transferred from a parent to offspring and is held to determine some characteristic of the offspring.