Check with your local electrical supply house, ifffffff thay have a UL approved underground splice kit, go for it butttttttttt I agree with the others, instead of splicing underground, Id at least consider bringing it above surface and splice in a weatherproof junction box. Your money your choice.
If the chart I looked at is correct, if thats No 6 copper wire and you pull 40 amps the voltage drop would be 6.5 volts !!!!!!!!!
Under older codes, for 120/240 volt single phase three wire service to a remote outbuilding you could get by with only three wires (L1 L2 Neutral), but nowadays most jurisdictions require four wires (L1 L2 Neutral Equipment Ground)
You may want to check with local authority if any exists where you live or your utility provider OR DO IT AND CHECK WITH NOBODY, YOUR CHOICE NONE OF OURS HERE.
Of course, the barns electrical service requires proper earth grounding (driven rod or rods, metallic utility pipes etc) REGARDLESS if three of four wire.
Post back any questions, check your local electrical supplier, consider checking with your utility provider or local authority, insure the barns service is earth grounded, take a look at your loads and see if voltage drop becomes an issue with 200 feet of No 6 wire???
Check to see how Billy Bob and Bubba would wire it???