Acharya Prashant addresses the issue of overthinking and anxiety by emphasizing the need for a sense of purpose and importance in life. He explains that the mind cannot tolerate a vacuum and will naturally fill any empty space with trivial, random thoughts or 'pathogens' like fear and worry. To counter this, one must develop a strong inner immunity by identifying what is truly worthy and important. When a person is deeply involved in a meaningful mission or work, they simply do not have the time or mental space to be bothered by everyday trivia or mental disturbances.