Let the number of sides of the regular polygon be n.

The interior angle of a regular polygon with n sides is given by the formula:

\(\frac{(n-2)180}{n}\) degrees.

The exterior angle is given by the formula \(\frac{360}{n}\) degrees. Since the interior angle is twice the exterior angle, we have:

\(\frac{(n-2)180}{n} = 2 \times \frac{360}{n}\)

Solving for \(n\), we find that:

n - 2 = 4

n = 6

So, the number of sides of the regular polygon is 6.