Step 1: Understand the process of aerobic cellular respiration. It is the metabolic pathway where glucose ($\mathrm{C_6H_{12}O_6}$) is broken down in the presence of oxygen ($\mathrm{O_2}$) to produce carbon dioxide ($\mathrm{CO_2}$), water ($\mathrm{H_2O}$), and energy in the form of ATP.
Step 2: Recall the general chemical equation for aerobic cellular respiration: $\mathrm{C_6H_{12}O_6} + 6\,\mathrm{O_2} \rightarrow 6\,\mathrm{CO_2} + 6\,\mathrm{H_2O} + \text{energy (ATP)}$. This equation represents the complete oxidation of glucose.
Step 3: Compare the given options to the general equation for aerobic cellular respiration. Identify which option matches the correct stoichiometry and products of the process.
Step 4: Eliminate incorrect options. For example, the equation $\mathrm{C_6H_{12}O_6} \rightarrow 2\,\mathrm{C_2H_5OH} + 2\,\mathrm{CO_2} + \text{energy}$ represents fermentation, not aerobic respiration. Similarly, $6\,\mathrm{CO_2} + 6\,\mathrm{H_2O} \rightarrow \mathrm{C_6H_{12}O_6} + 6\,\mathrm{O_2}$ represents photosynthesis, which is the reverse of respiration.
Step 5: Confirm that the correct equation for aerobic cellular respiration is $\mathrm{C_6H_{12}O_6} + 6\,\mathrm{O_2} \rightarrow 6\,\mathrm{CO_2} + 6\,\mathrm{H_2O} + \text{energy (ATP)}$, as it accurately describes the process of glucose oxidation in the presence of oxygen.