6. Variant 1 Sasha wrote the number 765476547654 on the board. He wants to erase several digits so that the remaining digits form the largest possible number divisible by 9. What is this number?
Answer: 7654765464.

Solution: The sum of the digits of the original number is $3 \cdot(7+6+5+4)=66$. According to the divisibility rule for 9, the sum of the erased digits must give a remainder of 3 when divided by 9. It is impossible to select digits with a sum of 3. Digits with a sum of $3+9=12$ can be chosen, and with a sum of $12+9=21$ or more, at least 3 digits can be taken. Among two numbers, the larger one is the one with more digits, so two digits with a sum of $12-7$ and 5 or 6 and 6 should be erased. Among two ten-digit numbers, the larger one is the one with larger digits in the higher positions. Therefore, the last "5" and the last "7" should be erased.

Variant 2 Sasha wrote the number 764576457645 on the board. He wants to erase several digits so that the remaining digits form the largest possible number divisible by 9. What is this number?

Answer: 7647645645.

Variant 3 Sasha wrote the number 674567456745 on the board. He wants to erase several digits so that the remaining digits form the largest possible number divisible by 9. What is this number?

Answer: 7457456745.

Variant 4 Sasha wrote the number 456745674567 on the board. He wants to erase several digits so that the remaining digits form the largest possible number divisible by 9. What is this number?

Answer: 4674567456.

Variant 5 Sasha wrote the number 546754675467 on the board. He wants to erase several digits so that the remaining digits form the largest possible number divisible by 9. What is this number?

Answer: 5475475467.