The correct answer is option 3: Cytokinin. Cytokinin is a plant hormone that plays a significant role in retarding the ageing of plant organs by controlling protein synthesis.

Let`s dissect the other options to understand why they are not correct:

Option 1: Abscisic acid, also known as ABA, is a plant hormone that is primarily involved in the regulation of plant responses to environmental stresses, such as drought and cold. While it does play a role in various physiological processes, it does not directly control protein synthesis to retard the ageing of plant organs.

Option 2: Auxin is a plant hormone that regulates various growth and developmental processes, such as cell elongation and root formation. It does not specifically retard the ageing of plant organs by controlling protein synthesis.

Option 4: Gibberellin is a plant hormone that promotes stem elongation, seed germination, and flowering. While it does regulate some aspects of plant growth and development, it does not have a direct role in retarding ageing by controlling protein synthesis.

In conclusion, cytokinin is the plant hormone that specifically controls protein synthesis to retard the ageing of plant organs.