Why does any numbers times 0 equal 0?

I prefer to think there's a basic rule that's not explained, and it goes like this: When we multiply something by zero, we're just saying it wrong, as zero actually trumps any number and has to be moved to the front of the equation. So, 6 x 0 isn't really what's being asked, it's 0 X 6. I have to think this way because if I hold 2 Cokes in my hand and multiply them by zero, I am still holding 2 Cokes. But if I have to imagine a zero trumps what I'm holding in my hand, the Cokes "disappear" (they become zero) and any number I follow with will now yield the proper answer, which is of course, zero. This is not a sly play on Coke Zero; I just saw that as I am proofreading. :)