Answer
$x=2k$
$y=2r$
$k,r \in \mathbb{Z}$
The difference: $|x−y| = 2|k-r|, that is a even number
Work Step by Step
Let $x$ and $y$ be two even integers, they both can be write as:
$x = 2k$
$y = 2r$
(with $k$ and $r$ being integers)
$k, r \in \mathbb{Z}$
Now we can subtract $x-y$:
If $x \geq y$:
$\begin{split}
x - y & = 2k - 2r \\
& = 2(k - r) \\
\end{split}$
If $x \lt y$ (Similar):
$\begin{split}
y - x & = 2r - 2k \\
& = 2(r - k) \\
\end{split}$
Since $k-r$ and $r-k$ are integers, then difference between $x$ and $y$ is even, by the definition of even numbers.
