SOLUTION

We are given that their sum is 24. So, we can write the equation:

x + (x+2) + (x+4) = 24

Simplifying this, we get:

3x + 6 = 24

Solving for x:

3x = 18

x = 6

Therefore, the three numbers are:

First number: x = 6

Second number: x+2 = 6+2 = 8

Third number: x+4 = 6+4 = 10

Now, let’s find their product:

6 * 8 * 10 = 480

So, the product of the three consecutive even integers is 480.