It's not that hard.

If you have -3 -3s and I give you one, you now only have -2 -3s. If you want to get to a total of -6, I have to hand over 4 more -3s to get there, the first 3 of them just being what's needed to get you to 0 and out of deficit. Now you get to hold onto the next two I hand over, and now you have 2 -3s which total -6. But that's 15 worth of -3s I had to hand over to get you there and -6 + 15 = 9, like -3 × -3 does too.

Negative numbers aren "real". Like 0, they're just a concept used to represent something, deficit.