On the assumption it's not written in treble or bass clef, but C clef instead, and you guessed it was treble, the Ab note would actually be a Bb. This then is enharmonically the same as A#, and also Cbb. That obviates the need for any (dubious in my opinion) bbb or #x.
Otherwise, the only notes with 3 enharmonic names are Ax/B/Cb; B#/C/Dbb; Dx/E/Fb; E#/F/Gbb, without going into 3#/b.
I'm going to be so bold as to say it wasn't an Ab. Or if it was, it's a non-question! Does happen...
EDIT - realised some more! D/Cx/Ebb; G/Fx/Abb and A/Gx/Bbb.
NEXT EDIT - the question would make sense if the clef was treble rather than bass, as that note becomes Fb.
LAST EDIT (I hope) - realised even more!! Eb/D#/Fbb; Bb/A#/Cbb; Gb/F#/Ex; Db/C#/Bx.So it may appear that actually the ONLY one which has just two names is the ONE IN THE QUESTION!!!
FINAL EDIT!!! - the correct answers are Gx and Bbb, because the actual question SHOULD have shown an A natural. RSL informed me just now that it is a typo.FINAL EDIT!!! - the correct answers are Gx and Bbb, because the actual question SHOULD have shown an A natural. RSL informed me just now that it is a typo.