Step 1: Fever with RBCs (blood) and pus cells in the stool indicates inflammatory or invasive diarrhoea, where the mucosa is damaged. We must pick the E. coli pathotype that produces this picture.
Step 2: Enterohaemorrhagic E. coli (EHEC, e.g. O157:H7) produces Shiga-like toxin and damages the colonic mucosa, giving bloody diarrhoea with inflammatory cells. Among the listed options it is the one causing this invasive, blood-and-pus type illness.
Step 3: The others give non-bloody, secretory diarrhoea: ETEC causes watery traveller's diarrhoea via heat-labile and heat-stable toxins, EPEC causes watery diarrhoea in infants by attaching and effacing lesions, and EAEC causes persistent watery diarrhoea by aggregative adherence. None typically gives RBCs and pus in stool.
Step 4: Therefore the causative organism is EHEC.