I’m going to exclude groundhogs from under a low deck (6 inches). How deep should I trench and put the wire before backfilling? Thanks

3". Deep enough to cover and any diggers hit it quickly and give up. It's also deep enough so a lawnmower won't catch it.
I had a friend that hired some Mexicans to trench 2 feet down. That just made the groundhog dig 2 feet before hitting it.

Edit: and if the digging sucks (rocks, roots, etc) just lay the screen down and bring in a load of crushed stone, loam, mulch or whatever you choose to cover it with. It beats digging, but you'll need a trailer or empty pickup to bring material to the job.

Good tip, Brian.

Thanks. This is more shallow than I thought I would have to go. You saved me some shovel time.

It is better to trap the occupants and remove them and not exclude them with a barrier in place. Exclusion allows them to return to their home easily and will cause you some quick dig in attempts. Unless you arent excluding in the true sense of the word.