find my number, if it is a two-digit one, one of its digits is 9, and it has remainder 0 when divided by 6.

If the remainder is 0 when divided by 6, then the number is divisible by 6.

A number is divisible by 6 when it's divisible by 2 and by 3. Since it's divisble by 2, it's even, and therefore it cannot have and odd number at ones place, so 9 must be on tens place. The number on ones place must be even and whole number must be divisible by 3. Therefore the sum of its digits must be divisible by 3. 9 is divisble by 3, so the number on ones place must also be divisble by 3, so their sum is divisible by 3. The only such number that is divisible by 3 and is even is 6. Therefore the whole number is 96.

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