For there to be palindromes, each digit must be replicated. Therefore there are at most three distinct digits.
If there are 3 pairs of different digits, then there are 6 palindromes. If there can be more duplicate digits, then there are 27 palindromes.
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Some 6 letter palindromes you may like:RedderHannah
6 if all digits are different, 27 otherwise.
987,654
6 digits
6