Looking at travel packages like this.
I am wondering, how does a '8 days 6 nights' package work? Where is the missing night?
Is the missing night in the flight towards the destination?
Days are counted from the day you leave to the day you come back (inclusive), while nights are nights spent in a hotel.
So "8 days, 6 nights" means you will have ~7 days at your destination and will spend one night on a plane.
The rule of thumb on day counting by tour companies is there is no rule of thumb.
Some count days actually doing something, so arriving in the late afternoon or departing after breakfast don't count setting up a tour of 5 days 6 nights ( but immigration would call it 7 days in country)
Some would count every day, so a 7 days 6 nights package.
Some will include flights which might include a night on the plane, but only count hotel nights, so you end up with 7 days 5 nights.
And of course each tour company considers their counting method to the "way it should be done".
The example you give lists the days pretty explicitly. They are counting the departure and travel day as part of the package.
Air Inclusive packages will count travel days, as in the example above.
Hotel Resort only packages will almost always count the shoulder days so Sunday to Saturday would be 7 Days & 6 Nights.
Cruise lines very rarely count the disembarkation day since you must be off the ship very early. They will list packages as 7 Days or 7 Nights even though you are technically on the ship 8 calendar days.
Trains will often list the duration in hours of the itinerary.