Explanation:

Let the speed of the water in still water = $x$

Given that speed of the stream = 3 kmph

Speed downstream $=\left(x+3\right)$ kmph

Speed upstream $=\left(x-3\right)$ kmph

He travels a certain distance downstream in 4 hour and come back in 6 hour.

ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour

since distance = speed × time, we have

$\left(x + 3\right)4 = \left(x - 3\right)6$

=>$\left(x + 3\right)2 = \left(x - 3\right)3$

=>$2x + 6 = 3x - 9$

=>$x = 6+9 = 15\text{ kmph}$