Orphanage
noun
You already learned that the word 孤児 means "orphan," so when you put a bunch of orphans in an institution it's called an orphanage.
こじいん
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
私は孤児院で幼少期を過ごしました。
I spent my childhood in an orphanage.