$$2H_2O_2(aq) \rightarrow 2H_2O(l) + O_2(g)$$

Explanation:

In this reaction, hydrogen peroxide decomposes into water and oxygen gas. The coefficients in front of each compound represent the relative number of molecules or moles of each substance involved in the reaction. To balance the equation, we need to make sure that the number of atoms of each element is the same on both sides of the equation.

Initially, we have 2 hydrogen atoms and 4 oxygen atoms on the left side of the equation. On the right side, we have 2 hydrogen atoms and 4 oxygen atoms in water, but only 2 oxygen atoms in oxygen gas. To balance the oxygen atoms, we need to add a coefficient of 2 in front of oxygen gas:

$$2H_2O_2(aq) \rightarrow 2H_2O(l) + 2O_2(g)$$

Now, we have 4 oxygen atoms on both sides of the equation. However, we still have 4 hydrogen atoms on the left side and only 2 hydrogen atoms on the right side. To balance the hydrogen atoms, we need to add a coefficient of 2 in front of water:

$$2H_2O_2(aq) \rightarrow 4H_2O(l) + 2O_2(g)$$

Now, the equation is balanced with 4 hydrogen atoms and 4 oxygen atoms on both sides.