Your explanation is missing some details. Does the game choose a random initial condition?
What do the ->0, ->1, and ->2 mean in your explanation of the color changes? Assuming the answers are "yes" and "nothing," this is a fairly standard heuristic search problem. Check any good AI book. The trick is coming up with a good heuristic function. Problems like this often submit to a search for a "macro operators." In this game you would look for a series of row/column flips that changes the color of exactly one square while letting all other squares exactly the same. This is a macro-operator. Once you discover such a series of moves, you just repeat it to get all 16 squares to the color you want (i.e. green). One game that submits very well to macro-move search is Rubik's Cube. Rober Korf's Ph.D. Dissertation (mid-80's) has the details.
