To solve this problem, we need to find the speed of the stream given the situation where a motorboat travels upstream and downstream at different speeds due to the presence of a stream. Here is the step-by-step solution:

1. Let the speed of the stream be \(x\) km/h.
2. The speed of the boat in still water is 15 km/h. Therefore, the effective speed downstream is \(15 + x\) km/h, and upstream, it is \(15 - x\) km/h.
3. According to the problem, the boat travels 20 km downstream and returns the same distance upstream in a total time of 4 hours. We can write two expressions for the time taken using the formula, \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\):
   • Downstream time: \(\frac{20}{15 + x}\) hours
   • Upstream time: \(\frac{20}{15 - x}\) hours
4. Given, the total time is 4 hours:
5. Finding a common denominator, this can be rewritten as:
6. Simplifying the numerator gives:
7. Resulting in:
8. Substitute \(15^2 = 225\):
9. Simplify:
10. Rearrange to solve for \(x^2\):
11. Further simplify:
12. Divide both sides by 4:
13. Take the square root of both sides:

Therefore, the speed of the stream is \(5\sqrt{3}\) km/h, which is the correct answer.