Answer
Overall reaction for alkaline battery:
$Zn(s) + 2MnO_{2} (s) + 2H_{2}O (l) -> Zn(OH)_{2}(s) + 2MnO(OH) (s)$
Work Step by Step
First, write half reactions.
Anode reaction (after balancing): $Zn(s) + 2OH^{-} -> Zn(OH)_{2} + 2e^{-}$
Cathode reaction (after balancing): $2MnO_{2} + 2H_{2}O + 2e^{-} -> 2MnO(OH) + 2OH^{-}$
Now, to eliminate e from both the equations, we have to add those two equations.
After adding two equations, we get
$Zn(s) + 2MnO_{2} (s) + 2H_{2}O (l) -> Zn(OH)_{2}(s) + 2MnO(OH) (s)$
This is the overall reaction that occurs in the alkaline battery.
