Balance the chemical equation for the combustion of methane: CH4 + O2 -> CO2 + H2O.

There is 1 carbon atom on the left side in $\text{CH}_4$ and 1 carbon atom on the right side in $\text{CO}_2$. Carbon atoms are already balanced.

$$\text{CH}_4 + \text{O}_2 \to \text{CO}_2 + \text{H}_2\text{O}$$

There are 4 hydrogen atoms on the left side in $\text{CH}_4$.
There are 2 hydrogen atoms on the right side in $\text{H}_2\text{O}$.
To balance hydrogen, place a coefficient of 2 in front of $\text{H}_2\text{O}$.

$$\text{CH}_4 + \text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}$$

Count oxygen atoms on the right side:
$\text{CO}_2$ has 2 oxygen atoms.
$2\text{H}_2\text{O}$ has $2 \times 1 = 2$ oxygen atoms.
Total oxygen atoms on the right side = $2 + 2 = 4$.
Count oxygen atoms on the left side:
$\text{O}_2$ has 2 oxygen atoms.
To balance oxygen, place a coefficient of 2 in front of $\text{O}_2$.

$$\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}$$

Left side:
Carbon: 1
Hydrogen: 4
Oxygen: $2 \times 2 = 4$
Right side:
Carbon: 1
Hydrogen: $2 \times 2 = 4$
Oxygen: $2 + (2 \times 1) = 4$
All atoms are balanced.

The balanced equation is:

$$\boxed{\text{CH}_4 + 2\text{O}_2 \to \text{CO}_2 + 2\text{H}_2\text{O}}$$