Well. Should you cross them or not? I'm so confused!
Last time I moved back to front, then crossed front-to-back.

 

Depends if your tires are unidirectional or not. Don't want to cross if you're unidirectional as now you have tires spinning the wrong way

Mine are not, so I cross them.

 

One note: based on the factory recommendation and personal experience front tires need higher air pressure than rears.
So as you rotate front-to-back remember to adjust your PSI for best results.
I know, not a big deal, but some people will go out of their way to maximize fuel economy and minimize tire wear, so there....
If you get your tires rotated at the dealer I can almost guarantee you they will skip that part.

Funny story - a friend of mine bought a brand new car couple of years ago and was complaining about choppy ride and general unpleasant feeling.
We checked tire pressure and all 4 wheels were at ~45 PSI.
For transport and storage that is okay, but the dealer should have fixed that while doing the PDI.

BTW, my Abarth was specified at 38PSI front 32PSI rear.
The car felt funny as hell after wheels were swapped front to back and they forgot to re-adjust.

 

When I first got my new car home I checked the tires next day and found the tires were about 6 psi low all the way around. The compact spare tire in the trunk was 20 psi low(!). The guys at the dealership had plenty of time to spend slapping dealership logos all over the rear end of my car but no time to spare checking the tire pressures. Good to see the dealership knows what it's priorities are.