Step 1: Begin by understanding the process of photosynthesis. Photosynthesis is the process by which plants, algae, and some bacteria convert light energy into chemical energy stored in glucose. The reactants are carbon dioxide (CO$_2$) and water (H$_2$O), and the products are glucose (C$_6$H$_{12}$O$_6$) and oxygen (O$_2$).
Step 2: Write the general chemical equation for photosynthesis. It is represented as: 6CO$_2$ + 6H$_2$O → C$_6$H$_{12}$O$_6$ + 6O$_2$. This equation shows that six molecules of carbon dioxide and six molecules of water are converted into one molecule of glucose and six molecules of oxygen.
Step 3: Compare the given options to the correct photosynthesis equation. The correct option should match the reactants (CO$_2$ and H$_2$O) and products (C$_6$H$_{12}$O$_6$ and O$_2$) in the correct proportions.
Step 4: Eliminate incorrect options. For example, the second option (6CO$_2$ + 6O$_2$ → C$_6$H$_{12}$O$_6$ + 6H$_2$O) incorrectly lists oxygen (O$_2$) as a reactant instead of water (H$_2$O). Similarly, the third and fourth options represent cellular respiration, not photosynthesis.
Step 5: Select the correct option that matches the photosynthesis equation: 6CO$_2$ + 6H$_2$O → C$_6$H$_{12}$O$_6$ + 6O$_2$. This correctly represents the reactants and products of photosynthesis.