Convert moles of magnesium nitride to grams: $$0.096 \, mol \, Mg_3N_2 \times \frac{100.9 \, g \, Mg_3N_2}{1 \, mol \, Mg_3N_2} = 9.69 \, g \, Mg_3N_2$$ So, 9.69 grams of magnesium nitride are needed to produce 11.6 grams of magnesium oxide. The final answer is $\boxed{9.69 \, g \, Mg_3N_2}$.
9.69 grams to be exact.