Step 1 :We are given that the difference of the squares of two consecutive even integers is 20. We can represent this mathematically as \((x+2)^2 - x^2 = 20\).
Step 2 :Solving this equation, we find that the solution to the equation is \(x = 4\).
Step 3 :This means that the two consecutive even integers are 4 and 6.
Step 4 :Final Answer: The two consecutive even integers are \(\boxed{4}\) and \(\boxed{6}\).