Answer
$Rate=-\frac{1}{2}\frac{\Delta[N_{2}O]}{\Delta t}=\frac{1}{2}\frac{\Delta[N_{2}]}{\Delta t}=\frac{\Delta[O_{2}]}{\Delta t}$
Work Step by Step
$\Delta$ represents change so ${\Delta t}$ means change in time. Rate is equal to the change in concentration over the change in time so for $O_{2}$ this is simply $\frac{\Delta[O_{2}]}{\Delta t}$. For $N_{2}O$ and $N_{2}$ the concentration changes twice as fast as that of $O_{2}$ because two moles of $N_{2}O$ decompse to make two moles of $N_{2}$ and only one mole of $O_{2}$. To fix this we multiply both by $\frac{1}{2}$. Also, $[N_{2}O]$ decreases as time passes so me have to multiply that expression by $-1$ to get the correct rate.
