Find the oxidation state of nitrogen in each species: N₂O, NO₂⁻, NO₃⁻, NH₄⁺, N₂H₄ and NH₂OH…

Step 1. $\text{N}_{2}\text{O}$. $2x + (-2) = 0$, so $x = +1$.

Step 2. $\text{NO}_{2}^{-}$. $x + 2(-2) = -1$, so $x = +3$.

Step 3. $\text{NO}_{3}^{-}$. $x + 3(-2) = -1$, so $x = +5$.

Step 4. $\text{NH}_{4}^{+}$. $x + 4(+1) = +1$, so $x = -3$.

Step 5. $\text{N}_{2}\text{H}_{4}$. $2x + 4(+1) = 0$, so $x = -2$.

Step 6. $\text{NH}_{2}\text{OH}$. $x + 2(+1) + (-2) + (+1) = 0$, so $x = -1$.