Step 1: Understand the concept of cellular respiration. Cellular respiration is a metabolic process 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 formula for cellular respiration. The balanced chemical equation for cellular respiration is: $\mathrm{C_6H_{12}O_6} + 6\,\mathrm{O_2} \rightarrow 6\,\mathrm{CO_2} + 6\,\mathrm{H_2O} + \text{energy}$. This equation represents the complete oxidation of glucose.
Step 3: Analyze the options provided. Compare each option to the general formula for cellular respiration. Eliminate options that do not match the reactants and products of cellular respiration.
Step 4: Verify the stoichiometry of the correct equation. Ensure that the number of atoms for each element is balanced on both sides of the equation. For example, glucose ($\mathrm{C_6H_{12}O_6}$) contains 6 carbon atoms, which are accounted for in the 6 molecules of carbon dioxide ($\mathrm{CO_2}$) produced.
Step 5: Confirm the correct answer. The balanced chemical equation for cellular respiration is: $\mathrm{C_6H_{12}O_6} + 6\,\mathrm{O_2} \rightarrow 6\,\mathrm{CO_2} + 6\,\mathrm{H_2O} + \text{energy}$. This matches the fourth option provided in the problem.