Please answer the question using Group Theory. Perhaps Burnside Lemma?

Suppose you have a circular cake which you cut into 6 equal pieces (in the normal way). Now, say you have 2 red candles and 2 blue candles which you want to place on the cake. How many ways can you do this? Note: Multiple candles can be placed on the same piece and we regard two pieces of the cake the same if they have the same amount of each colour of candle. Suppose you have a circular cake which you cut into 6 equal pieces (in the normal way). Now, say you have 2 red candles and 2 blue candles which you want to place on the cake. How many ways can you do this? Note: Multiple candles can be placed on the same piece and we regard two pieces of the cake the same if they have the same amount of each colour of candle