How to run 10/2 THHN outdoor wire
THHN = Thermoplastic HighHeat Nylon coated
THWN = same but water resistant
XHHW = cross linked polyethylene (i.e. PEX) for insulation = tougher than nylon
you imply stranded wire by saying THHN which in laymen's terms a single wire which per code (and common sense) must be run in some conduit or raceway meeting various requirements (for wire protection).
you say outdoor wire which would imply UF-B. Not unlike NM-B but UF-B is rated for outdoor exposure and burial in the ground, because it's insulation (unlike NM-B) can handle it. So a UF-B rated wire would be what u want it seems to not have to worry about fitting conduit.
note nommetalic sheathed cable (NM-B or UF-B) per article 334 prohibits above suspended ceilings in commercial occupancies because contractors are animals with pliers and saws, also any multi-family dwelling exceeding 3 floors.
What does the NEC require for finished basement wiring along the ceiling?
the NEC is more of a guide and not a how you must do it. There's room for interpretation based on various sections. If a finished occupied living space with a 7' ceiling within arm's reach then NM-B (or UF-B) would reasonably be a no because of likelihood to be contacted. But a ceiling > 8' out of arm's reach with NM-B supported properly (even by hooks) in a non living space would not be a hard no. a finished ceiling doesn't necessarily = finished basement. 334.15(b) = wiring be protected from physical damage by approved means (conduit) where necessary.