Predicting the products of reaction between ammonia and hydrogen peroxide
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Strong solutions of $\ce{H2O2}$ with a few drops of $\ce{NH4OH}$ (aq. ammonia) is left for 24 hours without any nitrite formation occurring. But upon longer standing, even with a small amount of hydroxide then nitrite forms. Nitrite also forms when a dilute solution of $\ce{H2O2}$ is mixed with $\ce{NH4OH}$  and is evaporated over pure conc. $\ce{H2SO4}$ with a bell jar. $\ce{H2O2}$ forms (even in very dilute solutions) nitrite very rapidly, if the $\ce{H2O2}$ solution is mixed with a few drops of $\ce{NH4OH}$ and a little $\ce{NaOH}$  and this then boiled in a retort to a very small volume. 

$\ce{2NO2- +  2H+(aq) &lt;=&gt; H2O + NO + NO2}$

$\ce{NO2- + NO3- + 2H+(aq) &lt;=&gt; H2O + NO2}$

Nitrogen dioxide is then able to attack ammonia.

$\ce{2NO2 + 2NO + 4NH3 -&gt; 2NH4NO2 + 2H2O + 2N2~~~~~~~~~~~~~~~~~~~~(1)}$

In any case, solutions of ammonium nitrite decompose on heating to 60 to 70C.

Perhaps the very slow spontaneous reaction of aqueous ammonia with $\ce{H2O2}$ takes place the small equilibrium with amide anions, $\ce{NH2-}$.

$\ce{NH2- + H2O2 -&gt; NH2- + 2OH-}$

Even in $\ce{NH4OH}$, there is a very slight equilibrium with amide ions.

$\ce{2NH3 &lt;=&gt; NH2- + NH4+}$

Amide rapidly and vigorously reacts with water, so the equilibrium of amide existence in water must be very low.

$\ce{NH2-+ H2O -&gt; NH3 + OH-}$ 

In the base catalysed decomposition of hydrogen peroxide, the mechanisms is presumably:-

$\ce{H2O2 + OH- -&gt; HOO- + H2O}$

$\ce{HOO- + H2O2 -&gt; HOOOH + OH-}$

$\ce{HOOOH --&gt; HOOO- + H+(aq)}$

$\ce{HOOO- -&gt; OH- + O2}$

Also, ammonium nitrite decomposes into nitrogen and water.

$\ce{NH4NO2 → N2 + 2 H2O~~~~~~~~~~~~~~~~~~~~~~~~~~(2)}$

A combination of ammonia and hydrogen peroxide is often used in the process of bleaching hair. Hydrogen peroxide has the necessary properties to remove the color from hair - it oxidizes one of hair’s melanin pigments to a colorless substance. This results in the hair becoming lighter. However, it is not recommended by hair professionals (those who don't understand chemistry but want your cash), and can cause extensive damage to hair (even causing it to fall out).

Therefore, the overall reaction is:-

$\ce{2(NH3•H2O) + 3H2O2 -&gt;[\Delta] N2 + 8H2O~~~~~~~~~~~~~~~~~~~~~~~(1) + (2)}$