Confusion with equations lol

It says that because x is a factor of 2x and xy, it must also be a factor of 2y. Why is it a factor of 2y? 
@WowJr
$$2x + 2y = xy $$
First of all:All three values (2x, 2y, xy) have a factor. A factor for the values can be x (hint mentions x so we'll stick with x, y is also fine though).
$$2 + {2y\over x} = y $$ $${2y\over x} = y  2 $$
Therefore:Because x and y are integers,
$${2y\over x} $$is an integer (y as an integer minus 2 as an integer leaves an integer result of 2y/x).
$$x*{2y\over x}=2y $$
Therefore x is a factor of 2y, where:Hope that helps.