Final answer:
Dr. Billings, as a psychoanalyst, would use techniques such as free association and dream interpretation, which are in line with Freud's methods for accessing and understanding the unconscious mind to treat psychological disturbances.
Step-by-step explanation:
Dr. Billings, as a therapist specializing in psychoanalysis, is likely to use techniques consistent with Freudian tradition. The techniques she is likely to employ include free association, dream interpretation, transference, and interpreting the client's resistance to discussing painful memories. These methods are rooted in Sigmund Freud's belief in the importance of accessing the unconscious mind to resolve repressed emotions and traumatic experiences from childhood that are manifesting as psychological disturbances. Psychoanalysis aims to help clients uncover and understand these unconscious motivations to facilitate healing and personal growth.