Hi and welcome to Reaper forums.
One (imo quite fast) way to do it:
But you have to set up a mouse modifier for this beforehand (only once though):
Go to Options -> Preferences -> (Editing behaviour) -> Mouse modifiers
and set it up like this:
Then make a time selection, hold this modifier combo (Shift + Win in this case) and drag the item to the other track (as shown in above gif).