How do I balance the following equation by the half-reaction method (it takes place in basic solution)?

Fe(OH)2(s) + O2(g) = Fe(OH)3(s)
the answer is 4Fe(OH)2(s) + 2H20(l) + O2(g) = 4Fe(OH)3(s) but how do I work it out?

Here is a set of rules for balancing half reactions in both acid and basic solutions.

http://www.chemteam.info/Redox/Redox.html

To balance the given equation using the half-reaction method in basic solution, you can follow these steps:

Step 1: Split the equation into two half-reactions.
a. Write the oxidation half-reaction, which shows the loss of electrons.
b. Write the reduction half-reaction, which shows the gain of electrons.

The given equation is: Fe(OH)2(s) + O2(g) = Fe(OH)3(s)

Step 2: Balance the atoms in each half-reaction.
a. Start by balancing all atoms, except for hydrogen and oxygen.
b. Balance the hydrogen atoms by adding H2O to the side deficient in hydrogen.
c. Balance the oxygen atoms by adding OH- ions to the side deficient in oxygen.

The half-reactions are as follows:

Reduction half-reaction: Fe(OH)2(s) = Fe(OH)3(s) + e-

Oxidation half-reaction: O2(g) + 2H2O(l) + 4e- = 4OH-

Step 3: Balance the electrons in the half-reactions.
In this step, the number of electrons lost in the oxidation half-reaction should be equal to the number of electrons gained in the reduction half-reaction.

Multiply the reduction half-reaction by 4 to balance the electrons:
4Fe(OH)2(s) = 4Fe(OH)3(s) + 4e-

Now, the number of electrons lost and gained is balanced.

Step 4: Balance the atoms in the overall reaction.
Match the number of atoms on both sides of the equation in the half-reactions.

The overall balanced equation is:
4Fe(OH)2(s) + 2H2O(l) + O2(g) = 4Fe(OH)3(s)

Now, you have successfully balanced the equation using the half-reaction method in basic solution.