The correct answer is option 4: They inhibit the release of egg.

Oral contraceptive pills work by using a combination of hormones (estrogen and progestin) or only progestin to prevent ovulation - the release of an egg from the ovary. When a woman takes these pills, the hormones in the pills regulate and suppress the natural hormonal cycle, preventing the ovaries from releasing an egg. Without an egg being released, fertilization cannot occur, meaning pregnancy is highly unlikely.

Option 1: They kill the egg - This is not correct, as oral contraceptive pills do not kill the egg. Rather, they prevent the release of the egg.

Option 2: They kill the sperm - This option is incorrect because oral contraceptive pills do not directly kill the sperm. Their main mechanism of action is preventing ovulation.

Option 3: They kill the zygote - This option is also incorrect as oral contraceptive pills do not kill the zygote. Their primary role is to prevent the release of an egg, thereby preventing fertilization and the formation of a zygote.

In conclusion, the mechanism of action of oral contraceptive pills is mainly to inhibit the release of an egg from the ovary.