Wetermine all possible replacements for digit $x$ so that the following number is divisible by 18 . $26668x$;
Divisibility by 18 will be determined by using which divisibility rules?
3 and 6
2 and 9
6 and 9
Therefore all possible replacements for digit $x$ are: $x\in \{$
(provide your answer as a list of digits in increasing order separated by a comma)

Step 1 ：In order to determine the possible replacements for digit $x$ so that the number $26668x$ is divisible by 18, we need to check the divisibility rules for 2, 3, and 9.

Step 2 ：For divisibility by 2, the last digit of the number must be even. Since the last digit is $x$, we need to find the even values for $x$.

Step 3 ：For divisibility by 3, the sum of the digits of the number must be divisible by 3. The sum of the digits of the number $26668x$ is $2+6+6+6+8+x$. We need to find the values of $x$ that make this sum divisible by 3.

Step 4 ：For divisibility by 9, the sum of the digits of the number must be divisible by 9. The sum of the digits of the number $26668x$ is $2+6+6+6+8+x$. We need to find the values of $x$ that make this sum divisible by 9.

Step 5 ：Let's find the possible values for $x$ that satisfy these conditions.

Step 6 ：possible_values = [8]

Step 7 ：Final Answer: The possible replacements for digit $x$ are $x\in \boxed{{\displaystyle \{8\}}}$.