Period after a sequence of transformations

Let $f: R \to R,\ f(x) = \cos\left(\dfrac{\pi}{6}x\right)\sin\left(\dfrac{\pi}{3}x\right)$.

Let $h: R \to R$ be the result of applying the following sequence of transformations to $f$:

1. a dilation by a factor of $\dfrac{1}{2}$ from the $y$-axis
2. a dilation by a factor of 2 from the $x$-axis
3. a translation of 2 units in the positive direction of the $x$-axis

The period of $h$ is