The fastest distribution of an injectable material or medicine, with minimal risk, is achieved by injecting it into the veins, making Option C the correct answer. Here’s why:

• Veins: When medicine is injected into the venous system (intravenously), it is quickly carried throughout the body by the bloodstream. The advantage of venous injection (IV injection) is the rapid onset of effects as the medicine is directly entered into the circulatory system, bypassing the need for absorption. This method also allows for precise control over the dosage and is used for substances that might be irritants or not effective if administered by other routes.
• Arteries: Injecting a substance directly into an artery is far more dangerous and is rarely done outside of specialized medical procedures. The arterial system is under much higher pressure than the venous system, which increases the risk of complications, including arterial damage and the potential for creating embolisms that could cause strokes or other serious issues.
• Muscles: Intramuscular injections are absorbed more slowly than intravenous injections because the blood flow to muscle tissues is less than to veins. This method is used for certain types of medication that need to be absorbed over a longer period. It's safer than arterial injection but slower in effect compared to venous injection.
• Lymph Vessels: The lymphatic system is not designed for the fast distribution of substances throughout the body. It has a much slower flow than the circulatory system and is involved in managing the immune response and transporting waste and other materials out of the bodily tissues. Injection into the lymphatic system is not a common practice for administering medications for systemic effect.

In summary, intravenous injection (Option C) is the preferred route for the immediate and safest distribution of injectable substances throughout the body.