What is the history of this six-armed image of Mahaprabhu? Kindly quote from proper source.
The shad bhuja murti form of Sri Chaitanya was revealed to Maharaja Prataparudra as described in Murari Gupta's Sri Krishna Chaitanya Charitra Mahakavyam:
While the king offered praise, Mahaprabhu, the protector of all sentient beings, displayed a radiant form of six-arms. That form was embellished by copious ornaments, and it revealed His own greatness. It was wonderful, magnificent and filled with immense oppulence.
Glory to the golden moon of Krsna Caitanya, who displays unbounded love, complete joy and ultimate charm. His eyes forever rove to and fro like bees in search of honey. Glory to the forever-blissful Nityananda, who is Balarama Himself. His personality is filled with divine sweetness, and intoxicated by Gaura-prema His form is sublimely personal and peaceful.
With His upper pair of hands, Gaurachandra brandished a bow and arrow, with the middle pair He held an excellent flute to His broad chest, and the lower pair of hands were held in a very graceful dancing posture. Thus the monarch saw the complete form of Gaurachandra, which was filled with love of Krsna. (Sri Krishna Chaitanya Charitra Mahakavyam, Canto 4, Chapter 16, Verses 13-15)