2006 mazdz rx8 shinka engine light is on, water is good, oil is good gas cap is tight

Get ahold of an OBDII scanner and get the code(s) read. Pretty much any auto parts store will let you use one. Write down the codes and post them back here so we can get you more help.

How long since you had maintenance on the engine? Are you keeping up? Are you racing it? If you drive the rotary hard, you will need to do servicing twice as often as the factory schedule- check plugs, wires, ignition, injectors, compression- the rotary is a beautiful, sensitive beast that needs a lot of attention- and if it has a lot of miles on it, you will eventually lose compression- the engines are easily replaced and I consider them almost like wearable parts-