1. Let $z = x + iy.$ Then $|z-3+2i| = |(x-3)+i(y+2)|.$ So the condition $|z-3+2i|\le 4$ represents all points $z$ lying inside or on the circle with:

   • centre $C=(3,-2)$
   • radius $r=4$.

2. We need the greatest and least values of $|z|$.

   Note that $|z|$ is the distance of the point $z=(x,y)$ from the origin $O=(0,0)$.

3. First find the distance of the centre from the origin: $OC = \sqrt{3^2+(-2)^2} = \sqrt{9+4}=\sqrt{13}.$

4. For a circle of radius $4$ whose centre is at distance $\sqrt{13}$ from the origin:

   • the maximum distance from the origin to a point on the circle is $\sqrt{13}+4,$
   • the minimum distance is $\big|\sqrt{13}-4\big|=4-\sqrt{13}$ since $4>\sqrt{13}$.

5. Therefore, $\text{greatest value of }|z|=4+\sqrt{13},$ $\text{least value of }|z|=4-\sqrt{13}.$

6. Their difference is $(4+\sqrt{13})-(4-\sqrt{13}) = 2\sqrt{13}.$

7. Checking options:

   • A: $2\sqrt{13}$ ✅
   • B: $8$ ❌
   • C: $4+\sqrt{13}$ ❌
   • D: $\sqrt{13}$ ❌

Hence the correct option is A.