Chatterbox knocked back six-pack in silence (6)
I believe the answer is:
gasbag
'chatterbox' is the definition.
(I've seen this before)
'knocked back six-pack in silence' is the wordplay.
'knocked back' shows that the letters should be reversed in order.
'six-pack' becomes 'abs' (short for abdominal muscles).
'in' means one lot of letters goes inside another.
'silence' becomes 'gag' (gagging is a kind of silencing).
'abs' inserted into 'gag' is 'gabsag'.
'gabsag' in reverse letter order is 'GASBAG'.
(Other definitions for gasbag that I've seen before include "He likes to talk" , "One talks incessantly about trivial things" , "Talkative type" , "Loudmouth - or balloon?" , "a container of helium" .)