Which of the following methods is prohibited due to its carcinogenic properties?

Methylene chloride is recognized for its carcinogenic properties, which is why its use is prohibited in certain applications, particularly in the context of lead paint removal and other similar tasks. This chemical solvent has been linked to increased cancer risk, making it a serious safety concern for both workers and the general public. The prohibition stems from extensive research and regulatory scrutiny that have identified it as a hazardous substance, prompting regulations to limit its use in order to protect health and safety.

Dry scraping, abrasive or grinding sanders, and heat guns, while they may pose other health risks related to lead exposure and dust generation, do not inherently contain carcinogenic components like methylene chloride. Therefore, they remain permissible under certain conditions with proper safety measures and controls in place, even though they still require caution to avoid lead exposure.