The interior angle of a regular polygon is twice its exterior angle. How many sides does the polygon have?

Let $I$ be the measure of one interior angle and $E$ be the measure of one exterior angle of a regular polygon.
We know that for any polygon, the sum of an interior angle and its corresponding exterior angle is $180^\circ$:

$$I + E = 180^\circ$$

We are given that the interior angle is twice the exterior angle:

$$I = 2E$$

Substitute the second equation into the first equation:

$$2E + E = 180^\circ$$ $$3E = 180^\circ$$ $$E = \frac{180^\circ}{3}$$ $$E = 60^\circ$$

For a regular polygon with $n$ sides, the measure of one exterior angle is given by the formula:

$$E = \frac{360^\circ}{n}$$

Substitute the value of $E$ we found:

$$60^\circ = \frac{360^\circ}{n}$$

Now, solve for $n$:

$$n = \frac{360^\circ}{60^\circ}$$ $$n = 6$$

The number of sides of the regular polygon is 6.

Comparing this with the given options:
A. 3
B. 8
C. 2
D. 6

The calculated number of sides matches option D.

The final answer is $\boxed{\text{D. 6}}$.