A challenge to accept women's promotion on the web (6)
I believe the answer is:
adware
'promotion on the web' is the definition.
'a challenge to accept women's' is the wordplay.
'challenge' becomes 'dare' (daring is a kind of challenging).
'to accept' means one lot of letters goes inside another.
'women' becomes 'w'.
'dare' enclosing 'w' is 'dware'.
'a'+'dware'='ADWARE'
(Other definitions for adware that I've seen before include "computer programs" , "computer plug-ins?" , "commercial apps" , "web advertising programs" .)