$$\left| {z - \left( {3 - 2i} \right)} \right| \le 4$$ represents a circle whose center is (3, $$-$$2) and radius = 4.

$$\left| z \right|$$ = $$\left| z -0\right|$$  represents the distance of point 'z' from origin (0, 0)



Suppose RS is the normal of the circle passing through origin 'O' and G is its center (3, $$-$$2).

Here, OR is the least distance

and OS is in the greatest distance

OR = RG $$-$$ OG and OS = OG + GS . . . . .(1)

As, RG = GS = 4

OG = $$\sqrt {{3^2} + \left( { - 2{)^2}} \right)} $$ = $$\sqrt {9 + 4} $$ = $$\sqrt {13} $$

From (1), OR = 4 $$-$$ $$\sqrt {13} $$ and OS = 4 + $$\sqrt {13} $$

So, required difference = $$\left( {4 + \sqrt {13} } \right)$$ $$-$$ $$\left( {4 - \sqrt {13} } \right)$$

= $$\sqrt {13} + \sqrt {13} $$ = $$2\sqrt {13} $$