Answer
See graph and explanations.
Work Step by Step
Step 1. Graph both $r=\frac{3}{2+6cos\theta}$ (red) and $r=\frac{3}{2+6cos(\theta+\frac{\pi}{3})}$ (blue) as shown in the figure.
Step 2. We can see that the blue curve is the result of the red curve rotated $\frac{\pi}{3}$ clockwise around the pole.
