Let's define the three consecutive even integers as:

$x, x+2, x+4$

According to the problem, the sum of these three integers is 246. We can set up the equation:

$x + (x + 2) + (x + 4) = 246$

Simplifying the left side:

$3x + 6 = 246$

Now, subtract 6 from both sides:

$3x = 240$

Divide both sides by 3:

$x = 80$

Thus, the three consecutive even integers are:

$x = 80, \quad x + 2 = 82, \quad x + 4 = 84$

So, the three numbers are 80, 82, and 84.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the equation change if the sum was for consecutive odd integers?
2. What happens if the sum is 300 instead of 246?
3. Can this problem be solved using algebraic expressions for odd integers instead?
4. What if four consecutive even integers were involved? How would you set that equation up?
5. How can this be generalized for the sum of any number of consecutive integers?

Tip: When working with consecutive integers, their expressions always follow a specific pattern, like $x, x+1, x+2$ for odd or $x, x+2, x+4$ for even numbers.