The product of ammonium chloride (NH₄Cl) and sodium hydroxide (NaOH) is ammonia (NH₃), water (H₂O), and sodium chloride (NaCl). This is a classic example of a double displacement reaction, where the positive and negative ions of two reactants swap places.

Here's the balanced chemical equation:

NH₄Cl (aq) + NaOH (aq) → NH₃ (g) + H₂O (l) + NaCl (aq)

Here's a breakdown of the reaction:

* Ammonium chloride (NH₄Cl) is a salt that dissolves in water to form ammonium ions (NH₄⁺) and chloride ions (Cl⁻).

* Sodium hydroxide (NaOH) is a strong base that dissolves in water to form sodium ions (Na⁺) and hydroxide ions (OH⁻).

* When these solutions are mixed, the ammonium ions (NH₄⁺) react with the hydroxide ions (OH⁻) to produce ammonia (NH₃) and water (H₂O). Ammonia is a gas, so it will be released from the solution.

* The remaining sodium ions (Na⁺) and chloride ions (Cl⁻) combine to form sodium chloride (NaCl), which remains dissolved in the solution.

Important Note: This reaction is an equilibrium reaction. The ammonia produced will escape as a gas, driving the reaction to the right, favoring the formation of products.