Which of the following is a well-known method for synthesizing methamphetamine?

The method involving Red Phosphorous is a well-known and historically significant technique for synthesizing methamphetamine. This process typically employs red phosphorus and iodine to reduce ephedrine or pseudoephedrine into methamphetamine. It is important to understand that this synthesis method has been common in illicit drug manufacturing due to the simplicity of the chemicals involved and the ability to manipulate freely available precursor substances.

Red phosphorus, often found in matchsticks or road flares, is used in a reaction that allows for the transformation of common cold medications into methamphetamine. The method's notoriety stems from its efficiency in producing significant yields of the drug while utilizing easily accessible materials, making it a favored choice among illicit chemists.

Other methods mentioned, like sodium reduction, electrolysis, and fractional distillation, do exist in various chemical synthesis contexts but are less commonly associated specifically with methamphetamine production in the way that the red phosphorus technique is. Additionally, these alternatives may require more complicated setups or less accessible reagents, further distinguishing red phosphorus as the correct choice in the context of this question about synthesizing methamphetamine.