Zero divided by zero is not zero?

Can someone explain this?

I mean, Imagine you have 0 cookies, and 0 people to share with. How many cookies will each person get? Zero, because you have no cookies and no people.

It's undefined since, for example(from Wikipedia):

6/3 = 2

And the opposite with multiplication to check the answer:

? * 3 = 6

So we know the answer to this is the "?" is 2.

But if you have for example, 6/0, then the new equation to check with multiplication makes no sense.

? * 0 = 6

Anything times 0 is 0(and not 6) so we can never solve for "?", so there is no solution, meaning 6/0 or anything divided by 0 is undefined.

And also if you had 0/0 the multiplication equation would be:

? * 0 = 0

There should only be 1 solution for "?", but now every number works, so this is still undefined.