Brigitte,
The above comments are worth paying attention to. The itinerary has too much doubling back on it. With (probably) 21-23 days, it would be best to fly into London first, then go to Paris or Amsterdam from there, and onward. Here is (just) my suggestion.
Starting with London, counting nights in a place (2 nights=one full day):
Day 1...Arrive London (sleep London)
Day2-3 London (sleep London)
Day 4 move to Amsterdam (Sleep Amsterdam)
Day5-6 Amsterdam (Sleep Amsterdam)
Day7 move to Paris(Sleep Paris)
Day8-10 Paris (Sleep Paris)
Day11 move to Prague (Sleep Prague)
Day12-13 Prague (Sleep Prague)
Day14 move to Vienna (Sleep Vienna)
Day15-16 Vienna (Sleep Vienna)
Day 17 move to Salzburg (Sleep Salzburg)
Day 18 Salzburg (Sleep Salzburg)
Day 19 move to Munich (Sleep Munich)
Days20-21 Munich (Sleep Munich)
Day 22 Fly home from Munich
This gives you: London 2 1/2 days, Amsterdam 2 1/2 days, Paris 3 1/2 days, Prague 2 1/2 days, Vienna 2 1/2 days, Salzburg 1 1/2 days, Munich 2 1/2 days. Each change of location will take a half day (or more, depending on mode of travel, time of day, etc.), hence the half days (travel and arrival days). You could add or subtract a day from one city or another.
With the amount of time you have, you may want to consider dropping one or more destinations altogether, to spend longer in a place. That is up to you and what you want to see and do in each city. There is no right or wrong way to do this trip. Just be aware that each move takes up more time from your trip than AI might calculate. Once you figure in these practicalities you might want to make adjustments. Each place you are going has so much to experience there that you may not want to shortchange it. Or this may be an introductory trip to whet your appetite for future travel. Whatever you decide on, have lots of fun and amusez-vous bien!