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 $x \in \boxed{\{8\}}$.