Answer: 99986420.

Solution. The number 99986420 meets the condition of the problem. Suppose there exists a larger eight-digit number. It is clear that its first three digits must be nines. Since there are only 5 even digits, the last five digits are $0,2,4,6,8$ in some order. But then such an eight-digit number cannot exceed 99986420, a contradiction.
Task 4.5. Write the largest eight-digit number in which all even digits are present. (Even digits: $0,2,4,6,8$.)