Timeline reasoning: depression has run for six months and is the core illness, while the auditory hallucinations are a recent, two-week add-on occurring inside that depressive episode. When psychosis sits entirely within a mood episode, the label is mood disorder with psychotic features, here psychotic depression.
Differentiate carefully. Schizoaffective disorder demands a stretch of psychosis (at least two weeks) when no major mood episode is present; that free-standing psychotic period is missing here, so it is excluded. Manic depressive (bipolar) illness needs a manic or hypomanic episode, which the patient never had. Schizophrenia would have psychosis as the primary, defining process rather than a brief feature trailing a long depression.
Because the hallucinations are confined to and explained by the depressive episode, the diagnosis is psychotic depression.
Ref: Arvind Arora Review of Psychiatry.