35.
There are 900 6-digit palindromes.
90000. With 10 digit palindromes, the last 5 digits are the same as the first 5 digits in reverse, eg 12345 54321. So it comes down to how many 5 digit numbers are there? They are the numbers "10000" to "99999", a total of 99999 - 10000 + 1 = 90000.
-1000
1-digit: 9 2-digit: 9 3-digit: 9 x 10 = 90 4-digit: 9 x 10 = 90 5-digit: 9 x 10 x 10 = 900 6-digit: 9 x 10 x 10 = 900