Answer
D = $\sqrt 7$
Work Step by Step
Step 1: Convert Polar points to Cartestian
P1: $(2, \pi/3)$
$x = rcosθ = 2\times cos(\pi/3) = 2\times \frac{1}{2} = 1$
$y = rsinθ = 2\times sin(\pi/3) = 2\times \frac{\sqrt 3}{2}= \sqrt 3$
P1: $(1, \sqrt 3)$
P2: $(4, 2\pi/3)$
P2: $x = rcosθ = 4\times cos(2\pi/3) = 4\times \frac{-1}{2} = -2$
$y = rsinθ = 4\times sin(2\pi/3) = 4\times \sqrt 3/2 = 2\sqrt 3$
P2: $(-1, 2\sqrt 3)$
Using the Distance Formula
D = $\sqrt ((x2-x1)^{2} + (y2-y1)^{2}) =\sqrt ((-1-1)^{2} + (2\sqrt3-\sqrt3)^{2}) $
D = $\sqrt7$
