Two-Night Stay
Staying For Two Nights
noun, verbal noun, の adjective
Two overnights is a two-night stay. In other words, you're staying for two nights.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
継母がうちに二泊泊めてくれって言ってるんだけど、どう思う？
My stepmother is asking if she can stay at our place for two nights, what do you think?