My brother downloaded a game on his ps4 console, and I would like to play that game on my console without buying it myself. Is this possible?
You simply have to sign in as the other users on your PS4. So long as you are logged in, you can play their games on their account. You will have to download the games they bought by going to "Library" and "Purchased". You should see all titles, demos, etc that You and THE OTHER USER have bought, then simply download the ones from their account.
Remember, you must be signed in the whole time to play the game that is on their profile.