Administrators and Analysts can move audiences, campaigns, and analyses between projects. Tags are automatically assigned to the project in which their associated campaign lives.
You can tell which project an audience is saved in from the Your Saved Audience page. To get there, from the Home Page, click the View All button on the Saved Audience tile. Then, find your audience, and on the audience tile, you'll see which project it is saved to. Click the arrow to modify and then choose your desired project from the list.
You can move campaigns and analyses between projects by following the same steps as moving an audience.