A number is divisible by 3 if you add up its digits and that is divisible by 3.
Example: 7263 is divisible by 3 because 7+2+6+3 = 18 and 18 is divisible by 3.
A number is divisible by 9 if you add up its digits and that is divisible by 9.
Example: 7263 is divisible by 9 because 7+2+6+3 = 18 and 18 is divisible by 9.
A number is divisible by 6 if it is an even number AND it is divisible by 3.
Example: 7263 is divisible by 3 because 7+2+6+3 = 18 and 18 is divisible by 3, but 7263 is not even, so it is not divisible by 6.
Example: 7362 is divisible by 3 because 7+3+6+2 = 18 and 18 is divisible by 3 AND 7362 IS even, so 7362 is divisible by 6.