Write instead of the stars digits so that the sum of the filled-in digits is odd and the following equality holds:

$$
42 \times * 8=2 * * *
$$

(L. Hozová)

Hint. Start with the first star.
We will sequentially substitute all possible digits in place of the first asterisk, calculate the product, and verify the other requirements:

- $42 \cdot 18=756$, the result is less than 2000; does not meet the criteria.
- $42 \cdot 28=1176$, the result is less than 2000; does not meet the criteria.
- $42 \cdot 38=1596$, the result is less than 2000; does not meet the criteria.
- $42 \cdot 48=2016$, the sum $4+0+1+6=11$ is odd; meets the criteria.
- $42 \cdot 58=2436$, the sum $5+4+3+6=18$ is even; does not meet the criteria.
- $42 \cdot 68=2856$, the sum $6+8+5+6=25$ is odd; meets the criteria.
- $42 \cdot 78=3276$, the result is greater than 2999; does not meet the criteria.
- the remaining two products are even larger; do not meet the criteria.

The problem has two solutions, namely

$$
42 \cdot 48=2016 \quad \text { and } \quad 42 \cdot 68=2856 .
$$