Answer
$$r = \frac{4}{{\cos \theta + 2\sin \theta }}$$
Work Step by Step
$$\eqalign{
& x + 2y = 4 \cr
& {\text{Use }}r\sin \theta = y{\text{ and }}r\cos \theta = x,{\text{ then}} \cr
& r\cos \theta + 2r\sin \theta = 4 \cr
& {\text{factor and solve for }}r \cr
& r\left( {\cos \theta + 2\sin \theta } \right) = 4 \cr
& r = \frac{4}{{\cos \theta + 2\sin \theta }} \cr} $$
