What part of the female anatomy produces eggs?

Ovaries - The ovaries are small, oval-shaped glands that are located on either side
of the uterus. The ovaries produce eggs and hormones.

HOW MANY EGGS DOES A WOMAN HAVE?

"During fetal life, there are about 6 million to 7 million eggs. From this time, no new eggs are produced.

The vast majority of the eggs within the ovaries steadily die, until they are depleted at menopause. At birth, there are approximately 1 million eggs; and by the time of puberty, only about 300,000 remain. Of these, 300 to 400 will be ovulated during a woman's reproductive lifetime. The eggs continue to degenerate during pregnancy, with the use of birth control pills, and in the presence or absence of regular menstrual cycles." conjgalscience.