Balancing half equations in an alkaline solution is different to balancing them in an acidic solutions, as we have been doing in the past.
In an acidic solution we balance for oxygen by adding water and balance for hydrogen by adding H⁺ ions.

However in an alkaline solution we balance for oxygen by adding either water or OH^- ions. But the trick is to know which one to use , water or the hydroxide ion.

A simpler approach is to write the half equation as if it were being done under acidic conditions just as you have been shown previously.

Once you have got a balanced half-equation, you then convert it to alkaline conditions by eliminating the H⁺ ions with the addition of hydroxide ions to both sides of the equation.

Lets see an example below.