2. Determine the largest even three-digit natural number whose product of digits is 24, and the digits are distinct.
First method:

The number 24 can be written as the product of 3 single-digit numbers in the following way:

$$
\begin{aligned}
24 & =2 \cdot 3 \cdot 4 \\
& =1 \cdot 4 \cdot 6
\end{aligned}
$$

$$
\begin{aligned}
& =1 \cdot 4 \cdot 6 \\
& =1 \cdot 3 \cdot 8
\end{aligned} \quad 3 \text { POINTS }
$$

Using these digits, the following three-digit even numbers can be written:

234, 324, 342, 432, 146, 164, 416, 614, 138, 318.

The largest even number among them is 614.