Adapted from my answer here:
Get the number of days between the Mondays of both weeks (using TRUNC( datevalue, 'IW' )
as an NLS_LANGUAGE
independent method of finding the Monday of the week) then add the day of the week (Monday = 1, Tuesday = 2, etc., to a maximum of 5 to ignore weekends) for the end date and subtract the day of the week for the start date. Like this:
SELECT ( TRUNC( end_date, 'IW' ) - TRUNC( start_date, 'IW' ) ) * 5 / 7
+ LEAST( end_date - TRUNC( end_date, 'IW' ) + 1, 5 )
- LEAST( start_date - TRUNC( start_date, 'IW' ) + 1, 5 )
AS WeekDaysDifference
FROM your_table