To find the minimum value of |z1-z2|, we need to consider all possible values of z1 and z2 that satisfy the given conditions.

Given conditions:
1. |z1| = 12
2. |z2-3-4i| = 5

Let's break down the problem step by step:

1. Finding the possible values of z1:
- The condition |z1| = 12 represents a circle centered at the origin with radius 12 in the complex plane.
- So, z1 can take any value on this circle.

2. Finding the possible values of z2:
- The condition |z2-3-4i| = 5 represents a circle centered at (3, 4) with radius 5 in the complex plane.
- So, z2 can take any value on this circle.

3. Finding the distance between z1 and z2:
- The distance between two complex numbers z1 and z2 is given by |z1-z2|.
- To minimize this distance, we need to find the closest possible values of z1 and z2, which lie on their respective circles.

4. Visualizing the problem:
- Plotting the circles representing the possible values of z1 and z2 on the complex plane will give us a better understanding of the problem.
- The circle representing z1 will have a radius of 12 and the circle representing z2 will have a radius of 5, centered at (3, 4).

5. Determining the closest points on the circles:
- The closest points on the circles will be the points where the line joining the centers of the circles is perpendicular to the line joining the centers of the circles.

6. Calculating the minimum distance:
- The minimum value of |z1-z2| will be the distance between the closest points on the circles.
- This distance can be calculated using the distance formula.

7. Final answer:
- After performing the calculations, we find that the minimum value of |z1-z2| is 2.

Therefore, the correct answer is option 'B'.