Tuition for private universities is more expensive than that of public universities.
Waseda University is a famous, private university in Japan.
The private college that’s on fire is the college I’m currently attending.
You've seen 私立, which is "private," and you've seen 大学, which is "college" or "university." So, combine them together and you have a private college / private university.
If you know the readings of the words 私立 and 大学 you'll be able to read this. It's also all jukugo on'yomi readings too, so you can read it that way.