In order to write the ionic equation, we must first assess the fact that MnO₂ is a solid, which does not dissociate into ions. Moreover, water will exist in its liquid form. Nitrous acid and manganese nitrate will exist as ions. Thus, the equation is:
MnO₂(s) + H⁺(aq) + NO₂⁻(aq) → Mn⁺²(aq) + NO₃⁻(aq) + H₂O(l)