Which single number proves that the claim 'every number that divides exactly by 3 also divides exactly by 6' is false?

To knock down a claim of the form 'every … is …' you need one example that satisfies the first part but fails the second. 9 divides exactly by 3 (9 ÷ 3 = 3) but not by 6, so it does the job. The traps: 12 and 18 divide exactly by both 3 and 6, so they obey the claim and cannot disprove anything; 8 does not divide by 3 at all, so the claim never applies to it and it proves nothing either way.