Let's analyze the given information before determining the distance between the two cars when they come to rest. Each car is traveling towards the other at a speed of $$20 \, \text{m s}^{-1}$$ and they both start braking when they are $$300 \, \text{m}$$ apart. The deceleration (negative acceleration) of each car is given as $$2 \, \text{m s}^{-2}.$$

To find the distance each car travels before coming to rest, we can use the kinematic equation that relates initial velocity ($$v_i$$), final velocity ($$v_f$$), acceleration ($$a$$), and distance ($$d$$), which is:

$$v_f^2 = v_i^2 + 2ad$$

Since the final velocity $$v_f = 0$$ (they come to rest), we can rearrange the equation to solve for $$d$$ (the distance each car travels before stopping):

$$0 = v_i^2 + 2ad \Rightarrow d = -\frac{v_i^2}{2a}$$

Plugging in the values for each car (noting that acceleration $$a$$ is negative because it is deceleration, so $$a = -2 \, \text{m s}^{-2}$$):

$$d = -\frac{(20)^2}{2(-2)} = -\frac{400}{-4} = 100 \, \text{m}$$

Each car travels $$100 \, \text{m}$$ before coming to rest. Since they both start $$300 \, \text{m}$$ apart and each travels $$100 \, \text{m}$$ towards the other, the total distance covered by both cars before stopping is $$2 \times 100 \, \text{m} = 200 \, \text{m}$$.

To find the distance between them when they come to rest, we subtract the total distance covered by both cars from the original distance between them:

$$300 \, \text{m} - 200 \, \text{m} = 100 \, \text{m}$$

So, the distance between the cars when they come to rest is $$100 \, \text{m}$$. Therefore, the correct option is:

Option B 100 m