What do you mean, auspicious day moving, long-term peace?

This sentence means: move to a new home, choose an auspicious day, make a complete arrangement, and expect to live and work in a new home and gain a lot.

"Moving on an auspicious day" means choosing an auspicious day to move, which means that I hope this day will bring good luck and auspiciousness to my new home. "Living and working in peace and contentment for a long time" means that you expect to live and work in peace and contentment in your new home, live a rich life and gain a lot. The whole sentence expresses good wishes and expectations for a new life.