The depth to which the ball will sink can be determined by considering the principle of buoyancy. According to Archimedes' principle, an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

1. Relative Density of the Ball:
The relative density of the ball is given as 0.8. Relative density is defined as the ratio of the density of the object to the density of the fluid. In this case, the density of the ball is 0.8 times the density of water.

2. Buoyant Force:
The buoyant force acting on the ball is equal to the weight of the water displaced by the ball. The weight of the water displaced can be calculated using the volume of the ball and the density of water.

3. Volume of the Ball:
To determine the volume of the ball, we need to know its mass and density. However, we are not given this information in the question. Therefore, we cannot directly calculate the volume of the ball.

4. Relationship between Volume and Relative Density:
We can use the concept of relative density to relate the volume of the ball to the volume of water displaced. Since the relative density is less than 1, it means that the ball is less dense than water. Therefore, the volume of the ball must be greater than the volume of water displaced.

5. Buoyant Force and Weight of the Ball:
Since the ball is less dense than water, the buoyant force acting on it will be less than its weight. This means that the ball will sink in water.

6. Determining the Depth:
Since the ball sinks, the buoyant force will be equal to the weight of the ball. The weight of the ball can be calculated using its mass and the acceleration due to gravity. However, we are not given the mass of the ball in the question.

7. Using the Principle of Buoyancy:
Since we cannot directly calculate the weight of the ball, we can use the principle of buoyancy to determine the depth to which the ball will sink. The depth to which the ball sinks is directly proportional to the volume of water displaced. Since the ball sinks completely, it displaces a volume of water equal to its own volume.

8. The Solution:
Since the ball is less dense than water and sinks, it will displace a volume of water equal to its own volume. Therefore, the depth to which the ball will sink is equal to its own diameter. Given that the ball falls from a height of 2m, the depth to which the ball will sink is 2m × 4 = 8m.

Thus, the correct answer is option 'A', 8m.