The name of a painting of a girl seated in a garden purple dress white hat head lowered so cannot see her face?

The painting you’re describing sounds like "Girl with a Pearl Earring" by Johannes Vermeer, although the specific details about the purple dress and white hat may not directly match this famous work. Alternatively, it could also resemble various Impressionist or Post-Impressionist artworks that depict young women in gardens. The head-down pose adds an air of mystery, typical of many portraits that focus on mood rather than facial features. If you're thinking of a specific artist or title, more details might help narrow it down!