The following are vegetative propagation: (a) Peanut seeds can germinate when buried in soil; (b) The male frog and the female frog embrace each other in the pond; (c) Begonia leaves can grow into new individuals; (4) A, using peanut seeds to reproduce offspring, through the combination of bisexual germ cells, belongs to sexual reproduction. A mistake;

B, the male and female frogs in the pond embrace each other, and after the hermaphroditic germ cells are combined, they belong to sexual reproduction. B error;

C. Begonia leaves can grow into new individuals, which belongs to asexual reproduction of plants with roots, stems, leaves and other vegetative organs. C is correct;

D, hens hatch chicks, which means that fertilized eggs hatch to get the next generation, and fertilized eggs combine with bisexual germ cells, which belongs to sexual reproduction. D error.

So choose: C.