Step 1: The question concerns the safe route for getting rid of cytotoxic agents and time-expired medicines, both of which are chemically hazardous.
Step 2: Such drug waste is handled by chemical disposal pathways - secured landfill after encapsulation or inertisation - rather than by methods designed for microbiological waste.
Step 3: Sterilisation by autoclave only inactivates infectious organisms and does nothing to neutralise toxic chemicals, while indiscriminate dumping risks leaching into soil and water.
Step 4: Plain burning is unsuitable for cytotoxics, so from the listed choices the appropriate engineered method is secured landfill.
\[\boxed{\text{Landfill (secured/engineered)}}\]