Question

The product of two consecutive positive even integers is 440. What are the integers?

Answer 1

If the average of the two integers is x, the product of the two integers is
  (x-1)(x+1) = 440
  x² - 1 = 440
  x² = 441 = 21²

21 is the odd integer between the two even integers you seek.

The integers are 20 and 22.

Answer 2

If intergers are n and n+2 we have the equation

n(n + 2) = 440
n^2 + 2n - 440 = 0
(n - 20)(n + 22) = 0

n = 20 , -22  (ignore the -22 because the integers are positive)

So the integers are 20,22