Answer
See graph below.
Work Step by Step
The question ONLY asks for a graph of the polar equation.
Given $r =2 - 2 \sqrt 2 \cos θ$
Table of Values:
$(2 - 2 \sqrt 2, 0)$
$(2 - \sqrt 2, \frac{\pi}{3})$
$(2, \frac{\pi}{2})$
$(2 + \sqrt 2, \frac{2\pi}{3})$
$(2 + 2\sqrt 2, \pi)$
$(2 + \sqrt 2, \frac{4\pi}{3})$
$(2, \frac{3\pi}{2})$
$(2 - \sqrt 2, \frac{5\pi}{3})$
See graph below. It is in the shape of a cardioid with a loop.