CW and CCW...are two different/opposite things...so I don't see how his would be able to have both/either screw on (unless his threads are so stripped that it's not really threading on).
If you're looking down the muzzle (don't shoot yourself in the eye
) and you screw on the suppressor "righty=tighty" then you have a CW threaded barrel...and need a CW threaded suppressor/flashhider/etc...
You could get a "gender bender" adapter that will change a CW thread to CCW thread...they typically add a bit of length to the outer barrel though.