Final answer:
The correct instrument for disengaging wire ties during the removal of an arch wire is the ligature cutter. While Howe pliers are also used in orthodontic procedures, they are not the best tool for cutting ligatures. Option 2.
Step-by-step explanation:
The instrument used to disengage wire ties when removing an arch wire in orthodontics is the ligature cutter. This tool is specifically designed for cutting through the small ligatures or wire ties that hold the arch wire in place on the brackets of braces. Howe pliers are also commonly used in orthodontics, but they are not primarily intended for cutting ligatures. They serve various purposes, such as adjusting wires, removing elastics, or placing and removing arch wires; however, ligature cutters are the precise tool for cutting wire ties.
Other options listed, such as Mosquito hemostat and Explorer, are not used for this specific function. The mosquito hemostat is usually used to clamp small vessels or grasp tissue, and the dental explorer is a diagnostic tool for detecting cavities and other aspects of dental health. Howe pliers could manipulate the wire but are not ideal for cutting the ligatures.