Backing crazy demand for material (6)
I believe the answer is:
damask
'for material' is the definition.
(damask is a kind of material)
'backing crazy demand' is the wordplay.
'backing' says the letters should be written in reverse.
'crazy' becomes 'mad' (synonyms).
'demand' becomes 'ask' (synonyms).
'mad' in reverse letter order is 'dam'.
'dam'+'ask'='DAMASK'
(Other definitions for damask that I've seen before include "reversible material" , "Heavy embroidered linen" , "Patterned material" , "A silk fabric" , "Red" .)