What method provides the best age constraint for the Sun, yielding approximately 4.6 billion years?

Asteroseismology.

When assessing the age of the Sun specifically, or stars closely resembling it (Sun-like stars), the technique offering the greatest precision is asteroseismology. By meticulously studying the internal sound wave frequencies generated by core processes, scientists can map the internal structural changes related to hydrogen depletion. This method provides constraints that are often better than 10% accurate. Applying this high-precision analysis to solar observations has constrained the Sun's age to approximately 4.6 billion years. While methods like main-sequence fitting offer only moderate precision (20-30%) and isochrone fitting for giants can be highly variable, asteroseismology provides the most robust measurement for this class of star.