Simplify. \[ \frac{\frac{6}{x^{2}}}{\frac{2 x-4}{x}} \]

To simplify the expression \[ \frac{\frac{6}{x^{2}}}{\frac{2 x-4}{x}}, \] we can start by rewriting it as a multiplication by the reciprocal. This means we will multiply the numerator by the reciprocal of the denominator: \[ \frac{6}{x^{2}} \div \frac{2x - 4}{x} = \frac{6}{x^{2}} \times \frac{x}{2x - 4}. \] Next, we simplify the denominator \(2x - 4\): \[ 2x - 4 = 2(x - 2). \] Now, substitute that back into the expression: \[ \frac{6}{x^{2}} \times \frac{x}{2(x - 2)}. \] Now we multiply the numerators and the denominators: \[ = \frac{6 \cdot x}{x^{2} \cdot 2(x - 2)} = \frac{6x}{2x^{2}(x - 2)}. \] Next, simplify \(6x\) and \(2\): \[ = \frac{3x}{x^{2}(x - 2)}. \] Now, we can simplify further by canceling \(x\) in the numerator and one \(x\) in the denominator, assuming \(x \neq 0\): \[ = \frac{3}{x(x - 2)}. \] Thus, the simplified expression is \[ \frac{3}{x(x - 2)}. \]