Japanese numbers are kinda complicated! But not really.
So this is one of those situations where a beginner learner is actually taught the different ways of saying Japanese numbers. They’re actually kind of important. What you’re not generally told is why.
So Japan actually has two different numbering systems. One of them is the native Japanese system (from before Chinese influence), and the other is the Chinese system. What appears to have happened is that the Japanese took the kanji from the Chinese system, bolted it onto their native numbering system, and called it a day. You’ll find this happens a lot, actually.
It seems arbitrary, but it’s kind of not. Probably the most important thing to note is that the only thing these numbering systems have in common with each other is that they represent numbers. So there will be a certain amount of memorization required. We can’t really avoid that.
But what we can point out is this: Several of the kanji have on-yomi (chinese) and kun-yomi (Japanese) readings – irrespective of the fact that they’re using the Chinese system. This appears to be because the Chinese readings sound too much like death, and the Japanese are a mite superstitious. So shi (four) becomes yon, because four in the Japanese reading is yottsu. Similarly, shichi (seven) becomes nana, because seven in the Japanese reading is nanatsu. So the important thing to note here is that some number kanji actually behave differently in jyukugo. The word for April, for example, is “shigatsu”, because in jyukugo you use the on-yomi readings.
Of course, as with everything else, there are a few things to memorize (like nine), but once you understand the nature of the different numbering systems, it becomes pretty simple to understand which numeral readings to use in which case.
Now, why they use the onyomi (or kunyomi versions of onyomi) readings for months, and native for days, is something to be looked up another day…