The term 'BIG NAME IN SPONGY TOYS' can be summarized as the brand Nerf, which is a four-letter word. Nerf is a toy brand owned by Hasbro that produces foam-based products such as balls, darts, and other items. It is known for its spongy material, making it safe for children to play with. Nerf has been around since the 1970s and has become a household name, making it a big name in spongy toys.