To prepare a 13.5N ammonium hydroxide solution, you would need to dilute concentrated ammonium hydroxide solution (typically 28-30% concentration) with water in the proper ratio to achieve the desired concentration. Calculate the volume of concentrated ammonium hydroxide and water needed based on the desired final volume of the solution and mixing the two components slowly to avoid splashing. Ensure to wear appropriate personal protective equipment and work in a well-ventilated area when handling these chemicals.