The preparation of potassium permanganate (\( {KMnO}_4 \)) from manganese dioxide (\( {MnO}_2 \)) involves two steps.
In the first step, \( {MnO}_2 \) reacts with potassium hydroxide (KOH) and potassium nitrate \(KNO_3\) to produce potassium manganate (\( {K}_2{MnO}_4 \)).
The reaction is: \[ {MnO}_2 + 4 {KOH} + 2 {KNO}_3 \to {K}_2{MnO}_4 + 2 {H}_2{O} \] Thus, the product of the first step is \( \boxed{K_2{MnO}_4} \), corresponding to option (4).