Sorry I don't know Access - but one of the following should work:
As your fetching the results back from the list box build up a SQL statement with something like ( you can use either 'and' or 'or' depending if it's cumulative or simply one on the options )
select field1, field2 from table1 where field3='value1' and field3='value2'
So each time you get a selection add on to your existing base statement starting with
'select field1, field2 from table1 '
the first time add ' where ' and then your clause field3=....
all subsequent times add ' and ' ( or ' or ') then your clause field3=...
Once you've add all the possibilities in then execute the statement generated.
Alternatively ( and preferably if Access supports it ) build a statement in a similar way but the statement will end up something like:
'select field1, field2 from table1 where field3 in ('value1', 'value2') '
this will return any row where field3 is any of the values ( same as 'or' in above ).