In RCC (Reinforced Cement Concrete) columns, both longitudinal reinforcement and lateral ties are provided to enhance the strength and stability of the column. The diameter of the lateral ties is an important consideration in ensuring the overall integrity of the column.

1. Purpose of Lateral Ties:
- Lateral ties, also known as transverse reinforcement or stirrups, are used to confine the longitudinal reinforcement in RCC columns.
- They help in preventing the longitudinal bars from buckling or spreading apart under axial loads, which can lead to the failure of the column.
- Lateral ties also provide additional strength and ductility to the column by effectively distributing the loads and restraining the concrete core from excessive deformation.

2. Selection of Lateral Tie Diameter:
- The diameter of the lateral ties is generally smaller than the diameter of the longitudinal reinforcement bars.
- It is important to select an appropriate diameter for the lateral ties to ensure proper confinement of the longitudinal bars and to allow for ease of construction.
- The ACI (American Concrete Institute) Code recommends that the lateral ties should have a minimum diameter of 8 times the diameter of the longitudinal bars or 8db.
- Here, "db" represents the diameter of the longitudinal bars.
- In the given question, the diameter of the longitudinal reinforcement is 32 mm.
- So, according to the ACI Code, the minimum diameter of the lateral ties should be 8 times 32 mm, which is equal to 256 mm.
- Among the given options, option 'C' with a diameter of 8 mm is the closest to the recommended minimum diameter of 256 mm.

3. Importance of Correct Lateral Tie Diameter:
- The correct diameter of the lateral ties is crucial for the proper functioning of the RCC column.
- Inadequate diameter of the lateral ties can lead to insufficient confinement of the longitudinal bars, resulting in decreased strength and ductility of the column.
- On the other hand, if the lateral ties are excessively large, it may lead to congestion and difficulty in placing the concrete during construction.
- Therefore, selecting the correct diameter of the lateral ties is necessary to ensure structural integrity, ease of construction, and compliance with the design codes and standards.

In conclusion, for an RCC column with a 32 mm diameter of longitudinal reinforcement, the recommended minimum diameter of the lateral ties is 8 mm, according to the ACI Code. This diameter ensures proper confinement of the longitudinal bars and facilitates ease of construction.