Given:
- The ratio between the length and breadth of the rectangular park is 3:2.
- A man cycling along the boundary of the park completes one round in 8 minutes.
- The speed of the man is 12 km/hr.

To find:
- The area of the park in square meters.

Let's solve the problem step by step:

Step 1: Calculate the speed of the man in meters per second.
- Convert the speed from km/hr to m/s by multiplying it by 5/18 (1 km/hr = 5/18 m/s).
- Speed in m/s = 12 * (5/18) = 20/3 m/s.

Step 2: Calculate the time taken by the man to complete one round.
- The time taken to complete one round is given as 8 minutes.
- Convert the time from minutes to seconds by multiplying it by 60 (1 minute = 60 seconds).
- Time in seconds = 8 * 60 = 480 seconds.

Step 3: Calculate the distance covered by the man in one round.
- The distance covered is the circumference of the rectangular park.
- The circumference of a rectangle is given by the formula: 2 * (length + breadth).
- Let's assume the length of the park is 3x and the breadth is 2x.
- Circumference = 2 * (3x + 2x) = 2 * 5x = 10x.

Step 4: Calculate the distance covered in meters.
- The distance covered by the man is given as 10x, which is the circumference of the park.
- Convert the distance from kilometers to meters by multiplying it by 1000 (1 km = 1000 m).
- Distance in meters = 10x * 1000 = 10000x.

Step 5: Calculate the time taken in seconds per meter.
- Time taken in seconds per meter = Time taken (in seconds) / Distance covered (in meters).
- Time taken in seconds per meter = 480 / (10000x).

Step 6: Calculate the speed in meters per second.
- Speed in meters per second = Distance covered (in meters) / Time taken (in seconds).
- Speed in meters per second = 10000x / 480.

Step 7: Equate the two expressions for speed in meters per second.
- Equating the two expressions:
20/3 = 10000x / 480.

Step 8: Solve the equation to find the value of x.
- Cross-multiply and solve the equation:
20 * 480 = 3 * 10000x.
9600 = 30000x.
x = 9600 / 30000.
x = 0.32.

Step 9: Calculate the length and breadth of the park.
- Length = 3x = 3 * 0.32 = 0.96.
- Breadth = 2x = 2 * 0.32 = 0.64.

Step 10: Calculate the area of the park.
- Area = Length * Breadth = 0.96 * 0.64 = 0.6144 square meters.

Therefore, the area of the park is 0.6144 square meters, which is equivalent to 614.4 square meters. However, none