I am trying to find a two 6-digit palindromes whose difference would be less than 50. Thank you!

How about:

099990
100001

Difference is 11

In general any two successive palindromes of the form

a9999a
(a+1)0000(a+1)

Have a difference of 11.

Or, if you don't think 099990 is a six-digit number, the leading and trailing 0 and 1 can be swapped with 1 and 2, 2 and 3, 3 and 4, etc. (e.g. 400004 and 399993).

Wasn't that last week's puzzler on Car Talk?