Rectangular coordinates: (0,-6)
Show me how to find the polar coordinates for this please.
Well you have not moved across at all, and gone down 6 units. Surely you can read off what the magnitude is. As for the angle, if you started from the positive x axis and went anticlockwise, what angle is swept out?
It's either $\displaystyle \displaystyle \begin{align*} \frac{3\pi}{2} \end{align*}$ if you move anticlockwise, or $\displaystyle \displaystyle \begin{align*} -\frac{\pi}{2} \end{align*}$ if you move clockwise. Generally we define $\displaystyle \displaystyle \begin{align*} \theta \in (-\pi, \pi] \end{align*}$, so choose $\displaystyle \displaystyle \begin{align*} -\frac{\pi}{2} \end{align*}$.
Now what is r?