Adult who's lost east of American city, carelessly (6)
I believe the answer is:
'carelessly' is the definition.
(I've seen this before)
'adult who's lost east of american city' is the wordplay.
'adult' becomes 'a' (abbreviation).
'lost' is an anagram indicator.
'east of' is a charade indicator (letters next to each other).
'american city' becomes 'ny' (I've seen this in other clues).
'who' with letters rearranged gives 'how'.
'how' put after 'ny' is 'nyhow'.
(Other definitions for anyhow that I've seen before include "in a mess", "In a careless manner", "Be that as it may", "Whatever's happened", "In no special way".)