2008 AMC 10A Problem 9

Suppose that
$\frac{2x}{3}-\frac{x}{6}$
is an integer. Which of the following statements must be true about $x$?

$\mathrm{(A)}\ \text{It is negative.}$
$\mathrm{(B)}\ \text{It is even, but not necessarily a multiple of 3.}$
$\mathrm{(C)}\ \text{It is a multiple of 3, but not necessarily even.}$
$\mathrm{(D)}\ \text{It is a multiple of 6, but not necessarily a multiple of 12.}$
$\mathrm{(E)}\ \text{It is a multiple of 12.}$