Step 1: Read the two anchors in the stem - a pus-like discharge from the male urethra and a smear showing gram negative cocci sitting inside the cells. Together they describe an organism that lives within neutrophils.
Step 2: That organism is Neisseria gonorrhoeae, a kidney-bean shaped gram negative diplococcus famous for being engulfed by pus cells. Its trademark presentation is acute urethritis with a thick purulent discharge, exactly as described.
Step 3: Rule the others out. Donovanosis is recognised by Donovan bodies in tissue, not by urethral diplococci. Bacterial vaginosis is a vaginal complaint with clue cells, irrelevant to a male urethra. Syphilis comes from a spirochete and starts as a painless ulcer, not a discharge.
Step 4: The picture of intracellular gram negative cocci plus purulent urethral discharge confirms gonorrhea.
\[\boxed{\text{Gonorrhea}}\]