That's right; a brown cover in a checked material (6)
I believe the answer is:
tartan
'checked material' is the definition.
'tartan' can be an answer for 'checked' (I've seen this before). I am unsure of the 'material' bit.
'that's right a brown cover in a' is the wordplay.
'that's right' becomes 'R' (common abbreviation).
'a brown cover' becomes 'tat' (I can't explain this - if you can you should believe this answer much more).
'in' means one lot of letters goes inside another.
'a' becomes 'an'.
'r' put inside 'tat' is 'tart'.
'tart'+'an'='TARTAN'
Can you help me to learn more?
(Other definitions for tartan that I've seen before include "Woollen fabric with plaid design" , "Cloth with a plaid design" , "Scottish plaid design" , "Scots material" , "Symbol of the Scottish clans." .)