Problems with hat back to front: Miss Woodhouse's? (8)
I believe the answer is:
dilemmas
'problems' is the definition.
(I've seen this before)
'with hat back to front miss woodhouse's?' is the wordplay.
'with' says to put letters next to each other.
'hat' becomes 'lid' (lid can informally mean a hat).
'back to front' says the letters should be written backwards.
'miss woodhouse's?' becomes 'Emmas' (main character in Jane Austen's novel Emma).
'lid' written backwards gives 'dil'.
'dil' next to 'emmas' is 'DILEMMAS'.
(Other definitions for dilemmas that I've seen before include "Situations involving difficult choices" , "Problems for dismal me" , "Predicaments or quandaries" , "Am misled into quandaries" .)