Answer: (9) chemical, (10) heat, (11) mechanical, (12) electrical, (13) electrical, (14) light
Explanation: As seen in the diagram, there is fuel being burned. This fuel is the gas, oil, or coal. These chemicals have chemical energy that will be converted into heat energy when burned, just like how you convert chemical energy from firewood into heat energy when you burn the firewood. The steam produced when the heat energy boils the water moves through the turbine, causing the turbine to spin, which in turn spins the generator because the generator is connected to the turbine. Mechanical energy is both the kinetic energy and potential energy of an object. Kinetic energy is the energy an object has when it is moving, so the rotating turbine and generator have kinetic energy and thus mechanical energy. Generators turn kinetic energy into electrical energy by having coils inside of it spin around and around in a magnetic field, producing an electromotive force (aka voltage) that produces current and thus electricity within the loop. Obviously, light bulbs convert electrical energy into light energy, and they illuminate the world around us.
Additional Note: Technically, the electrical energy turns into thermal energy inside of the light bulb filament, causing the light bulb filament to get so hot that the filament radiates visible light. Due to the light bulb filament being hot, the space inside of the light bulb consists of either a vacuum or inert gases. Regular air contains oxygen and thus will react with the hot metal filament of the light bulb, oxidizing the light bulb filament and thus making the light bulb filament brittle. The brittle light bulb filament will then break and cause the light bulb to no longer radiate light.