...to figure out discharging methods at hospital (2,3,5)

'to figure out discharging' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'methods at hospital' is the wordplay.
I cannot really understand how this works, but
'at' is within the answer.
'hospital' could be 'h' (abbreviation for hospital) and 'h' is found within the answer.
an anagram of 'methods' is 'dotemhs' which is present in the left over letters.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?