Step 1: Hypopyon (a layer of pus in the anterior chamber) appearing a couple of days after intraocular surgery is acute postoperative endophthalmitis until proven otherwise. Diabetics are at higher risk. This is a sight-threatening emergency, so options (b), (c) and (d) are inappropriate as first-line care.
Step 2: The eye coats and barriers limit how much drug reaches the vitreous from topical or systemic routes, so therapeutic levels at the infected site demand direct delivery. The standard of care is an immediate vitreous tap for culture followed by intravitreal antibiotics (typically vancomycin plus ceftazidime/amikacin), which makes option (a) correct.
Step 3: Eye drops alone (b) cannot achieve adequate vitreous concentration and would let the infection progress. Vitrectomy (c) is reserved for severe cases (for example vision of light perception only, per the Endophthalmitis Vitrectomy Study) and is not the universal initial step. "No treatment" (d) risks rapid, permanent vision loss.