If the digits are not allowed to repeat in any number formed by...

We have to form a number greater than $10, 000$ by using the digits $0, 2, 4, 6, 8,$ hence, the first place of the number can't be zero.

Thus, for the first place we have $4$ choices i.e. $2, 4, 6, 8$ and the remaining places can be filled with any of the digits, thus we have respectively $4, 3, 2, 1$ choices.

Hence, using the fundamental principle of multiplication, the total numbers which are greater than $10, 000$ are

$= 4 \times 4 \times 3 \times 2 = 96 .$