Third day or day three. No matter how you look at this word, it makes a lot of sense.

This is a jukugo word, which usually means on'yomi readings from the kanji. Counting days, however, are an exception (at least up to ten). You need to use the kun'yomi readings to read this word. You already know the kun'yomi reading for 三 from when you learned the word 三つ. Here is a way to remember the reading for 日:

On the third day you have to give me (み) a ride in your car (か). I don't have a car of my own, so don't forget me, okay?