Multiplying
Noun, する verb, and の adjective
はんしょく
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?
Something that is overgrown and will multiply is obviously breeding and multiplying a ton.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.