To understand the given statements, let's first discuss the concepts of metacentric height, center of gravity, and center of buoyancy.

1. Metacentric Height:
The metacentric height (GM) is a measure of the stability of a floating body, such as a ship. It represents the distance between the center of gravity (CG) and the metacenter. The metacenter is the intersection point of the vertical line passing through the center of buoyancy (CB) in the initial equilibrium position and the vertical line passing through the center of buoyancy in the heeled position.

2. Center of Gravity:
The center of gravity (CG) is the point where the entire weight of a body can be considered to act. It is the average position of all the individual particles of the body, each having a weight.

3. Center of Buoyancy:
The center of buoyancy (CB) is the centroid of the displaced volume of fluid. It represents the point where the buoyant force acting on a body can be considered to act.

Now, let's analyze each statement and determine their correctness:

Statement 1: Filling up a part of the empty hold of a ship with ballasts will reduce the metacentric height.
This statement is correct. By adding ballasts to the hold of a ship, the weight distribution changes, which affects the position of the center of gravity. As the center of gravity moves downwards, the metacentric height decreases, resulting in reduced stability.

Statement 2: Filling up a part of the empty hold of a ship with ballasts will lower the position of the center of gravity.
This statement is incorrect. Adding ballasts to the hold of a ship does not lower the position of the center of gravity. Instead, it shifts the center of gravity downwards due to the added weight. Thus, the position of the center of gravity is lowered indirectly.

Statement 3: Filling up a part of the empty hold of a ship with ballasts will elevate the position of the center of gravity.
This statement is incorrect. As mentioned earlier, adding ballasts to the hold of a ship shifts the center of gravity downwards. Therefore, the position of the center of gravity is actually lowered, not elevated.

Statement 4: Filling up a part of the empty hold of a ship with ballasts will elevate the position of the center of buoyancy.
This statement is correct. When ballasts are added to the hold of a ship, the weight distribution changes, and the center of buoyancy is affected. The center of buoyancy moves upwards, elevating its position.

To summarize, the correct statements are:
- Filling up a part of the empty hold of a ship with ballasts will reduce the metacentric height.
- Filling up a part of the empty hold of a ship with ballasts will elevate the position of the center of buoyancy.

Hence, the correct option is D) 2 and 4 are correct.