Attempting to balance a redox reaction using half reactions leaves an unbalanced component
It seems likely that you are starting with the wrong half reactions.

Since this reaction happens in water, separate the ionic species into their ions:

$$\ce{Mg(NO3)2 -&gt; Mg^{2+} + 2NO3-}$$

$$\ce{HNO3 -&gt; H+ + NO3-}$$

Now, one half reaction should involve magnesium (and have no nitrogen anywhere). The other half reaction should involve nitrogen only.

$$\ce{Mg -&gt; Mg^{2+}}$$
$$\ce{NO3- -&gt; N2O}$$