12. (10 points) Find the largest five-digit positive integer that is not a multiple of 11, and from which no number that can be divided by 11 can be obtained by deleting some of its digits.
【Analysis】The largest five-digit number, according to the characteristic of being divisible by 11, the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11. Therefore, a five-digit number cannot be divisible by 11, and we can first determine the digit in the ten-thousands place, then determine the other digits one by one. If this five-digit number is 90000, it is clearly not divisible by 11, so the largest five-digit number that meets the condition must be greater than 90000. If $b=9$, then $\overline{99 \mathrm{cde}}$ becomes 99 after removing $\overline{\mathrm{cde}}$, which is divisible by 11, so $b \neq 9$. If $b=8$, then $\overline{98 \mathrm{cde}}$ becomes 98 after removing cde, which is not divisible by 11, $\therefore b=8$, and 88 is not suitable,
$\therefore c=7, \overline{987 \mathrm{de}}$ becomes 987 after removing several digits, which cannot be divisible by 11,
If $d=9,8,$ or 7, none of them are suitable, when $d=6$, $\overline{9876 \mathrm{e}}$ becomes 9876 after removing several digits, which cannot be divisible by 11, $\therefore d=6$ If $e=9,8,7$ or 6, none of them are suitable, so $e=5$,

In summary, this five-digit number is: 98765