According to my NEC table 310 #6 copper UF and NM-B are not quite up to the task of powering a 48 amp EVSE having a maximum ampacity of 55 amps. #6 THHN (run through conduit) is good for 75 amps. #6 Aluminum or copper clad aluminum is a straight up fire hazard on a 60 amp circuit.
It might work just fine, but your local electrical inspector will likely be unhappy. I'd avoid any sharp bends in the wire contacting wall edges or corners because it's going to run hot and a pinch point could melt through the casing.
(I own a house that predates electrification which has been wired over the past century by both highly skilled professionals and some less than highly talented amateurs. That put me on a first name basis with the local electrical inspector and we had many discussions about what was dangerous, what was 100 years old but quite safe, and what was dodgy but not worth touching.)
