To find the equation of the curve, we need to integrate the derivative \(\frac{dy}{dx} = \frac{8}{(3x + 2)^2}\).

The integral of \(\frac{8}{(3x + 2)^2}\) is \(-\frac{8}{3(3x + 2)} + c\), where \(c\) is the constant of integration.

Given that the curve passes through the point \((2, 5\frac{2}{3})\), we substitute \(x = 2\) and \(y = 5\frac{2}{3}\) into the equation:

\(5\frac{2}{3} = -\frac{8}{3(3 \times 2 + 2)} + c\)

\(5\frac{2}{3} = -\frac{8}{12} + c\)

\(5\frac{2}{3} = -\frac{2}{3} + c\)

Solving for \(c\), we get \(c = 6\).

Thus, the equation of the curve is \(y = -\frac{8}{3(3x+2)} + 6\).