How come they are able to use the number without the counting things symbol つ? Shouldn’t they have to say やっつ here instead of はち?
I tried googling this and I just found a bunch of pages listing when to use つ, which is like… most of the time. I figured I understood when to use it. The other two context sentences make perfect sense to me, using it for “page eight” and “eight o’clock”. But the sentence I quoted goes against my intuitive understanding of when not to use the numbers that don’t have つ.
It is using a counter actually, just a more specific one. There are a bunch of counters that are used for different categories of things, which you’ll get a feel for over time. In this case, こ is the counter. I found a tofugu article on it, actually:
So yes you’re totally right, you do a need a counter in a case like that; it just won’t always be in the form of ～つ!
はっこ is how you pronounce 八個. There are patterns to how numbers are combined with counters, but there’s also a lot of exceptions. It means “eight (small) things”, compared to はち which means “eight (as an abstract concept)” and やっつ which is “eight things” with the generic counter.
Edit: for comparison, the equivalent of 一つ using 個 is 一個 which is pronounced いっこ.