It's 3 wires. Two conductors and a ground.
3/4" of any type conduit will suffice.
I wonder what the last person was thinking, laying it out with no conduit. Can't imagine what possessed
I need 60 Amps. It's my understand that 6 Gauge Romex NM wire is only good for 55 Amps.
True, but irrelevant. NM-B cable is forced to use the 60 degree C thermal rating (55A).
THHN running in conduit can generally run at 75 degrees C (65A). But check the connections. If any of those are rated 60C, you must pigtail with a 75C rated splice (like a MAC Block, a good choice for a 6 AWG splice).
When you are provisioning load, you must respect the thermal limit. So in your case if you need to provision 60A, 55A won't cut it; you must do what's required to qualify for 75C operation.
If no breaker is made at that size, you round up to the next available breaker.