Quantity of handouts distributed (8)
I believe the answer is:
thousand
'quantity' is the definition.
(thousand is a kind of quantity)
'handouts distributed' is the wordplay.
'distributed' indicates an anagram.
'handouts' is an anagram of 'THOUSAND'.
'of' is the link.
(Other definitions for thousand that I've seen before include "in MCC, but missing double century" , "Large number" , "a fair amount?" , "quite a lot" , "cube" .)