Let the two consecutive even numbers be $x$ and $x + 2$.

The product of these two numbers is $x(x + 2) = x^2 + 2x$.

According to the problem, this product is 12 more than the square of the smaller number, which gives us the equation:

$x^2 + 2x = x^2 + 12$

Now, subtract $x^2$ from both sides:

$2x = 12$

Divide both sides by 2:

$x = 6$

So, the smaller number is 6, and the consecutive even number is $6 + 2 = 8$.

Thus, the two consecutive even numbers are 6 and 8.

Would you like any details or further explanation?

Here are some related questions:

1. What is the general formula for consecutive even numbers?
2. How do we handle similar problems involving odd numbers?
3. Can we solve this equation graphically?
4. How can we check if a solution is correct for similar problems?
5. What is a method for solving word problems in algebra?

Tip: When dealing with consecutive numbers, always assign variables carefully and translate word problems into equations accurately.