Explanation:

- The man can swim in still water at a speed of 6 km/h.

- Swimming upstream takes him thrice as long as swimming downstream.

- Let x be the speed of the stream.

- Downstream speed = (6 + x) km/h.

- Upstream speed = (6 - x) km/h.

Given the time relation:

- Time downstream = Distance / (6 + x)

- Time upstream = Distance / (6 - x) = 3 times Time downstream

Setting up the equation:

- Distance / (6 - x) = 3 * Distance / (6 + x)

- Simplifying gives: 6 - x = (6 + x) / 3

- Solving this results in x = 3 km/h

So, Speed downstream = 6 + 3 = 9 km/h

Option 3: 9 km/h is correct.