8.4. How many natural numbers less than 1000 are divisible by 4 and do not contain the digits $1,3,4,5,7,9$ in their notation?
8.4. The desired numbers are written only with the digits $0,2,6,8$.

There is exactly one single-digit number that satisfies the condition, which is the number 8.

There are six two-digit numbers, which are $20,28,60,68,80,88$.

The desired three-digit numbers can end with the following 8 combinations of digits: $00,08,20,28,60,68,80,88$. In each of these variants, the first place can be occupied by any of the three digits $2,6,8$. Thus, we get $3 \cdot 8=24$ desired three-digit numbers.

Therefore, the total number of such numbers is $1+6+24=31$.

Answer: 31