My mother will be admitted to a nursing home next spring.
Please write down your admission date here.
My yakuza boss is in jail now.
You enter a place. So, you have been given (or forced) admission into this place. You have been given entrance. For example, "admission" into a prison is something you could gain by not doing your WaniKani reviews in certain Crabigator ruled countries.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.