The correct answer is option 4, the endoplasmic reticulum.

The endoplasmic reticulum (ER) is a network of membranous tubules and sacs that spreads throughout the cytoplasm of eukaryotic cells. It plays a crucial role in the transportation of materials within the cell.

On the surface of the ER, there are ribosomes (option 1), which are responsible for protein synthesis. While ribosomes are involved in protein production, they are not directly involved in the movement of materials throughout the cell.

Mitochondria (option 2) are the powerhouses of the cell, producing energy in the form of ATP. Although they are involved in many cellular processes, they are not primarily responsible for the movement of materials.

Lysosomes (option 3) are cell organelles containing digestive enzymes. They primarily function in intracellular digestion and waste removal, rather than material transportation.

Therefore, the correct answer to the question is option 4, the endoplasmic reticulum, which is responsible for the movement of materials to different parts of the cytoplasm and nucleus.