Correct option: Stage IV.
Step 1: The Hinchey classification grades complicated diverticulitis by the extent and nature of the peritoneal contamination.
Step 2: The four stages are: I, mesenteric or pericolic abscess; II, pelvic (walled-off) abscess; III, generalised purulent peritonitis; IV, generalised faecal peritonitis.
Step 3: This patient has frank faecal peritonitis, which is the most severe grade, so it is Hinchey stage IV. This carries the highest mortality and usually mandates a Hartmann procedure.
Why not stage III: Stage III is purulent (pus) peritonitis without free faecal soiling; the presence of faeces upgrades it to stage IV.
Ref: Bailey and Love, Short Practice of Surgery, 27th edition, 2018.