How to find a product of two consecutive even integers whose sum is a number?

Any even integer takes the form , where is any integer. Even integers occur every two integers following some even integer. This means the next even integer will take the form .

So you want to find .

If you're told that the two integers add to some number, call it , then we also know



and from that we can solve for , which is exactly what we need to know in order to get a concrete value for the product above. In particular,



and so