The private kindergartens are closed on the Christmas Day.
Go out of here and walk left along the street until you come to the third intersection and you'll get to the private hospital.
I found out that the guy Koichi secretly met at the cafe was a private detective.
The place where I stand is my own private area. Think of the "circle of personal space." This is where you stand plus an arm's length. This area is very private to you. Who knows what you do in your own private area.
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.