6. \( \frac{3\left(x y^{6}\right)^{0}}{-6 y^{2}} \)

Any expression raised to the power of zero equals one, provided that the base is not zero. Therefore, \( \left(x y^{6}\right)^{0} = 1 \). This simplifies your original expression to: \[ \frac{3 \cdot 1}{-6y^{2}} = \frac{3}{-6y^{2}} = -\frac{1}{2y^{2}}. \] So the simplified form is: \[ -\frac{1}{2y^{2}}. \] If you're looking for clarity in your calculations, remember that powers of zero are a trusty travel companion in math – they always lead you back to one! Just like packing light for a trip, simplifying might take some items out of the equation but makes everything easier to handle.