Can I transfer purchased apps from my iPhone 6 to my new iPhone Xs? If so, how?

Make sure your signed into the same Apple ID on the iPhone Xs as on the iPhone 6. Go to the App Store. Tap on the icon in the upper right (if you have a picture representing yourself in your Apple ID, it will be there). Tape on "Purchased". Download anything not on the phone that you want.

Yes.

You can restore a backup from the 6 onto the Xs and this will set all your downloaded apps to redownload on the X in roughly the same places they were on on the 6:

See here: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Or redownload them manually from your purchased history, assuming you are using the same Apple ID for both iPhones.

See here: Redownload apps, music, movies, TV shows, and books - Apple Support