6÷3=2, 6÷2=3, 6÷1=6… As you make the divisor smaller and smaller, the quotient gets larger and larger. If you keep bringing the divisor closer to 0, the quotient just keeps growing without bound — it does not settle on one particular number. Use the slider to bring the divisor closer to 0 yourself.
Another way: check it backward using multiplication. To check whether "6÷2=3" is correct, see whether 2×3=6. Then, to check "6÷0=?", you would need to find a number that makes 0×(?)=6. But multiplying 0 by any number always gives 0, so you can never get 6 — in other words, the answer does not exist.
There is an even stranger case. To check "0÷0=?", you would need to find a number that makes 0×(?)=0. But this time, any number works (0×5=0, 0×100=0…) — the answer cannot be uniquely determined. Since neither case has one definite answer, mathematics simply defines division by 0 as "undefined."