Answer: 96
Explanation:
You can think a 9-digit palindrome as 5 slots.
In each slot, you can put a digit.
_ _ _ _ _
The first slot, is the 9th digit and the 1st digit.
The second slot is the 8th digit and the 2nd digit
etc.
This is for the nature of a palindrome number.
Then, we have 5 selections.
Now, remember that for the first four selections each digit will appear two times, so we can choose each even number only once.
Then:
For the first selection, we have 4 options (2, 4, 6 and 8. The zero can not be chosen here because the 9th digit can not be a zero if this is a nine digit number).
For the second selection we have 4 options, the 3 that remain for the previous selection and the 0, that is even.
for the third selection, we have 3 options.
for the second selection, we have 2 options
for the fifth selection we have only one option.
The total number of combinations is equal to the product of the number of options in each selection, this is:
C = 4*4*3*2*1 = 96