To find the equation of the curve, we need to integrate the given derivative \(\frac{dy}{dx} = -\frac{8}{x^3} - 1\).

Integrate \(\frac{dy}{dx}\) with respect to \(x\):

\(y = \int \left( -\frac{8}{x^3} - 1 \right) \, dx\)

\(y = \int -8x^{-3} \, dx - \int 1 \, dx\)

\(y = -8 \int x^{-3} \, dx - \int 1 \, dx\)

\(y = -8 \left( \frac{x^{-2}}{-2} \right) - x + c\)

\(y = 4x^{-2} - x + c\)

\(y = \frac{4}{x^2} - x + c\)

Given that the point (2, 4) lies on the curve, substitute \(x = 2\) and \(y = 4\) to find \(c\):

\(4 = \frac{4}{2^2} - 2 + c\)

\(4 = 1 - 2 + c\)

\(4 = -1 + c\)

\(c = 5\)

Thus, the equation of the curve is \(y = \frac{4}{x^2} - x + 5\).