How do you balance redox reactions in the basic solution?

Hint: The redox reaction involves oxidation reaction and reduction reaction simultaneously. In the redox reaction, the transfer of charge takes place. For balancing the redox reaction in the basic solution, the hydroxide ion is added.

Complete step by step answer:
The redox reaction is defined as the reaction where the oxidation and reduction takes place simultaneously.
The oxidation is defined as the loss of electrons and reduction is defined as the gain of electrons.
The bases on dissolving in water gives hydroxide ion $O{H^ - }$. So, for balancing the redox reaction in the basic solution requires hydroxide ion.
Take an example of redox reaction:
$Ag(s) + Z{n^{2 + }}(aq) \to A{g_2}O(aq) + Zn(s)$
To balance the given redox reaction in basic condition, following steps are involved.
(1) Separate the two half of the redox reaction:
Oxidation half: $Ag(s) \to A{g_2}O(aq)$
Reduction half: $Z{n^{2 + }}(aq) \to Zn(s)$
(2) Balance the elements other than oxygen O and hydrogen H.
$2Ag(s) \to A{g_2}O(aq)$
$Z{n^{2 + }}(aq) \to Zn(s)$
(3) Balance the oxygen atom by adding water ${H_2}O$
${H_2}O(l) + 2Ag(s) \to A{g_2}O(aq)$
$Z{n^{2 + }}(aq) \to Zn(s)$
(4) Balance the hydrogen by adding the proton
\[{H_2}O(l) + 2Ag(s) \to A{g_2}O(aq) + 2{H^ + }(aq)\]
$Z{n^{2 + }}(aq) \to Zn(s)$
(5) Balance the charge with electron
\[{H_2}O(l) + 2Ag(s) \to A{g_2}O(aq) + 2{H^ + }(aq) + 2{e^ - }\]
$Z{n^{2 + }}(aq) + 2{e^ - } \to Zn(s)$
(6) Add the reactions and cancel the electrons
\[{H_2}O(l) + 2Ag(s) + Z{n^{2 + }}(aq) \to Zn(s) + A{g_2}O(aq) + 2{H^ + }(aq)\]
(7) Add hydroxide ion to balance the hydrogen ion. As two hydrogen ions are present, two hydroxide ions are added.
\[{H_2}O(l) + 2Ag(s) + Z{n^{2 + }}(aq) + 2O{H^ - } \to Zn(s) + A{g_2}O(aq) + 2{H^ + }(aq) + 2O{H^ - }(aq)\]
(8) Combine the hydroxide ion and hydrogen ion on the same side to form water.
\[{H_2}O(l) + 2Ag(s) + Z{n^{2 + }}(aq) + 2O{H^ - } \to Zn(s) + A{g_2}O(aq) + 2{H_2}O(l)\]
(9) Cancel the common terms to get the overall reaction.
\[2Ag(s) + Z{n^{2 + }}(aq) + 2O{H^ - } \to Zn(s) + A{g_2}O(aq) + {H_2}O(l)\]

Note:
Make sure to follow each step during balancing the redox reaction. When the charge of the atoms are balanced by the electrons after that make sure to scale the reaction so they contain equal numbers of electrons. In this example, it was already done.