The question asks about the primary function of the structure labeled 'A' in the diagram. The image shows a rough endoplasmic reticulum (RER) with ribosomes attached to its surface, indicated as structure 'A'.

Let's analyze the functions of the structures and options provided:

1. Production of fat molecules: This function is typically associated with the smooth endoplasmic reticulum (SER), not the rough endoplasmic reticulum (RER). The RER is not involved in lipid synthesis.
2. Manufacturing proteins: Ribosomes, which are the small particles attached to the RER, are responsible for protein synthesis. Therefore, the RER, with its ribosomes, is primarily involved in manufacturing proteins. This makes this option correct.
3. Storing genetic material: Storage of genetic material occurs in the cell nucleus, not the endoplasmic reticulum.
4. Digestion of food particles: This is a function of lysosomes, not the RER.

Given this analysis, the correct answer is that the primary function of the structure 'A' (ribosomes on the rough endoplasmic reticulum) is Manufacturing proteins.