cheapest way and safe to run 6-3 underground 75 ft to my garrage to a sub panel, sub panel will have its oun outside ground, so do i need to run the 6-3 w g or is 6-2 with the comon ok? is romex ok if i put it in a condoit, pvc a foot deep ok? or do i need the uf wire?
thank you for time and help, richard

You should use the 6-3 wire regardless of local grounding. That is the wire that will signal the breakers in the house to click off in the event of a short to ground. The NEC allows only from pole to meter, and meter to panel without ground, all others must have a continuous ground.

Romex is probably a bad idea. You can get spools of #6 THHN or cut length. In conduit, the insulation on romex poses additional problems that may interfere with NEC requirements, best to use individual wires pulled through conduit that are rated for wet applications. Probably need 1" conduit for #6 with ground. (Can be upwards of 3" with sheathed wires like romex)

You have the option of using direct burial wire. Granger has some #6 UF-B that may suit your application. Direct burial must rated for wet applications, and still contain a ground. You should still protect the wire with piping where it goes from dirt to home and dirt to garage, but you don't need piping all the way if you use direct burial rated wires.

1 foot deep is sufficient for conduit. The conduit provides some extra protection against shovels and whatnot, with UF rated cable, 24" is recommended.

Check your local codes though. I lived in one area where electrical lines needed to be 24" regardless of application, where I live now, you can get away with 6" below grade in conduit.

It doesn't hurt to call local electric/gas companies to check for buried wires and pipes too.