Yes, supply from lines is 120 bit typically between 110-115 at the outlet. I apologize, I simplified in my head and didn’t explain.
Peter, I think you are still missing the boat on this. You told him to replace his two 30amp breakers with 1 60 amp breaker. He doesn’t have two breakers. He has 1 30amp 2 pole breaker (2 30amp breakers tied together per the OP). if he had 2 30A 2 pole breakers he could replace with 1 60A 2 pole breaker but in his terms that would be 4 30A breakers tied together.
As UC mentioned, the wires for a 30A circuit are likely 10ga NM-B (romex). You need 4ga for 60A.
At the end of the day, he is running a new circuit to a new location for an outlet. Unless he has the skills and knowledge to turn off power, remove the existing wiring for dryer circuit, size new circuit and wiring within max capacity, run new wire from panel to new location, and install an outlet then he should be contacting an electrician, telling the what he would ideally have and then let the electrician decide what works with his electrical system and install that. Asking questions on this forum about who to seek guidance from is great, taking advice and doing work yourself is a great way to burn your house down if you don’t understand what you are doing.