Given:
- Speed of the boat in still water = 18 km/h

To find:
- Speed of the stream

Assumption:
- Let the speed of the stream be 'x' km/h

Explanation:
- When the boat is moving downstream, it gets the additional speed of the stream which helps it to cover more distance in the same time compared to still water.
- When the boat is moving upstream, it has to overcome the speed of the stream which reduces its effective speed.

Formula:
- Speed downstream = Speed of boat in still water + Speed of stream
- Speed upstream = Speed of boat in still water - Speed of stream

Given:
- Distance = 12 km
- Time taken upstream = Time taken downstream + 1/2 hour

Calculation:
- Let's assume the speed of the stream is 'x' km/h

- Speed downstream = Speed of boat in still water + Speed of stream
=> Speed downstream = 18 + x km/h

- Speed upstream = Speed of boat in still water - Speed of stream
=> Speed upstream = 18 - x km/h

- Time taken downstream = Distance / Speed downstream
=> Time taken downstream = 12 / (18 + x) hours

- Time taken upstream = Distance / Speed upstream
=> Time taken upstream = 12 / (18 - x) hours

- Time taken upstream = Time taken downstream + 1/2 hour
=> 12 / (18 - x) = 12 / (18 + x) + 1/2

- Cross multiplying the equation:
12(18 + x) = 12(18 - x) + 1/2(18 + x)(18 - x)

- Simplifying the equation:
216 + 12x = 216 - 12x + 324 - x^2/2

- Combining like terms:
24x = 108 - x^2/2

- Multiplying the equation by 2 to remove the fraction:
48x = 216 - x^2

- Rearranging the equation:
x^2 + 48x - 216 = 0

- Solving the quadratic equation, we get:
x = 3 km/h or x = -51 km/h (ignoring the negative value)

Conclusion:
- The speed of the stream is 3 km/h.