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

First, integrate \(\frac{3}{\sqrt{x}}\):

\(\int \frac{3}{\sqrt{x}} \, dx = \int 3x^{-1/2} \, dx = 6\sqrt{x} + C_1\).

Next, integrate \(-x\):

\(\int -x \, dx = -\frac{x^2}{2} + C_2\).

Combining these, the general solution is:

\(y = 6\sqrt{x} - \frac{x^2}{2} + C\).

Given the point (4, 6), substitute \(x = 4\) and \(y = 6\) to find \(C\):

\(6 = 6\sqrt{4} - \frac{4^2}{2} + C\).

\(6 = 12 - 8 + C\).

\(C = 2\).

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