Given \(\frac{dy}{dx} = \frac{6}{x^2}\), we need to find \(y\) by integrating \(\frac{dy}{dx}\).

Integrate \(\frac{dy}{dx} = \frac{6}{x^2}\):

\(y = \int \frac{6}{x^2} \, dx = \int 6x^{-2} \, dx\)

\(y = 6 \cdot \left( \frac{x^{-1}}{-1} \right) + c = -6x^{-1} + c\)

Using the point \((2, 9)\) to find \(c\):

\(9 = -6(2)^{-1} + c\)

\(9 = -3 + c\)

\(c = 12\)

Thus, the equation of the curve is \(y = -6x^{-1} + 12\).