Can I use 6AWG THHN Wire for a 60 Amp Sub Panel?

there is an online chart for that ... search for wire size chart with distance. for usual 220v single phase feed ... no. use #4 to prevent significant voltage drop

#6 is OK for 60 amps.  Be sure your subpanel has enough slots for all of the circuits you will be adding in the future.  You might want to consider 100 amps and #4 and not have to worry.  Be sure and put the right size circuit breaker in the upstream existing panel to protect the USE cable, regardless of all of the breakers in the subpanel.  The breaker protects the downstream wire, and you will eventually have enough circuits in the shop to overload the USE cable.  So you need a breaker in the existing panel to protect this cable.  Check that you do have space for this breaker.  A 100 amp and 60 amp take up the same amount of space, so that is why you want to go big so that you will have the capacity for the future. I think the THHN is for overhead cable.   Are you in a ditch or overhead?  50 feet is a long ways for the mast on the side of a shop.  You may need a pole and then drop down into the shop.