Breeding
Multiplying
noun, する verb, の adjective
Something that is overgrown and will multiply is obviously breeding and multiplying a ton.
はんしょく
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
本当に俺たちの柴犬を繁殖させることができると思う？
Do you really think we can breed our own Shiba dogs?