Acharya Prashant explains the four stages of spiritual progress: listening, reflection, deep contemplation, and equanimity. Listening involves receiving knowledge from a teacher, while reflection is the process of using one's own intellect and logic to become convinced of that truth. Reflection is limited by the boundaries of the mind and the individual's past experiences. Deep contemplation occurs when the reflected truth moves from the conscious thinking mind into the subconscious or intuitive mind, becoming a background presence in one's life. Finally, equanimity is reached when the mind itself dissolves, leading to complete clarity and the resolution of all problems.