Fire'n Ice © 1993 Tecmo, Limited.
North American release. Game developed in Japan. See the original Famicom version for more information: Solomon no Kagi 2 - Coolmintou Kyuushutsu Sakusen.
Description from the back cover:
If you like puzzles and logic, you're going to love Fire 'n Ice!
Fire monsters are loose on Coolmint Island. You must use your wits and skill to clear each level and defeat the wicked wizard. Beware! You might find yourself extremely hooked on this wildly addictive puzzle game!
GAME ID: NES-K2-USA
Released in March 1993 in the USA.
Game's ROM.