The property that can be used to expand the expression \( 5(3x - \frac{6}{7}) \) is the Distributive Property.
Regarding the second part of your question:
If a student expanded the expression \(-6(4x - \frac{2}{13})\) and made an error, the correct answer would be:
No, the student should have multiplied \(4x\) and \(-\frac{2}{13}\) by \(-6\).
This means each term inside the parentheses should be multiplied by \(-6\), resulting in \(-6 \cdot 4x\) and \(-6 \cdot -\frac{2}{13}\).