To balance the equation for CH4 + O2 -> CO2 + H2O, we need to make sure that the number of atoms of each element is the same on both sides of the equation. Here's the step-by-step process:

Start with the unbalanced equation:

```

CH4 + O2 -> CO2 + H2O

```

Step 1: Balance carbon atoms

There is 1 carbon atom on the left side and 1 carbon atom on the right side, so we don't need to change anything.

Step 2: Balance hydrogen atoms

There are 4 hydrogen atoms on the left side and 2 hydrogen atoms on the right side. To balance this, we'll need to put a coefficient of 2 in front of the H2O molecule.

```

CH4 + O2 -> CO2 + 2H2O

```

Step 3: Balance oxygen atoms

There are 2 oxygen atoms on the left side and 3 oxygen atoms on the right side. To balance this, we'll need to put a coefficient of 2 in front of the O2 molecule.

```

CH4 + 2O2 -> CO2 + 2H2O

```

Step 4: Check all atoms

Now, we have 1 carbon atom, 4 hydrogen atoms, and 4 oxygen atoms on both sides of the equation, so it is balanced.

The final balanced equation is:

```

CH4 + 2O2 -> CO2 + 2H2O

```