Answer
$r = 4-4~cos~\theta$
This graph is a cardiod.
We can see this graph below:
Work Step by Step
$r = 4-4~cos~\theta$
When $\theta = 0^{\circ}$, then $r = 4-4~cos~0^{\circ} = 0$
When $\theta = 60^{\circ}$, then $r = 4-4~cos~60^{\circ} = 2$
When $\theta = 90^{\circ}$, then $r = 4-4~cos~90^{\circ} = 4$
When $\theta = 120^{\circ}$, then $r = 4-4~cos~120^{\circ} = 6$
When $\theta = 180^{\circ}$, then $r = 4-4~cos~180^{\circ} = 8$
When $\theta = 240^{\circ}$, then $r = 4-4~cos~240^{\circ} = 6$
When $\theta = 270^{\circ}$, then $r = 4-4~cos~270^{\circ} = 4$
When $\theta = 300^{\circ}$, then $r = 4-4~cos~300^{\circ} = 2$
Since $\frac{4}{4} = 1$, this graph is a cardiod.
We can see this graph below:
