Box on right shows sign of damage (6)
I believe the answer is:
crater
'sign of damage' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.
'box on right' is the wordplay.
'box' becomes 'crate' (crate is a kind of box).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'right' becomes 'r' (abbreviation).
'crate'+'r'='CRATER'
'shows' is the link.
Can you help me to learn more?
(Other definitions for crater that I've seen before include "Pit resulting from impact or explosion" , "Hole (on the moon?)" , "Bowl-shaped cavity as on volcano peak" , "Bomb-hole" , "Bowl-shaped hole in the ground" .)