To find the equation of the curve, we need to integrate the derivative \(\frac{dy}{dx} = x^{-\frac{1}{2}} - 3\).

The integral of \(x^{-\frac{1}{2}}\) is \(2x^{\frac{1}{2}}\), and the integral of \(-3\) is \(-3x\).

Thus, the general solution is \(y = 2x^{\frac{1}{2}} - 3x + c\), where \(c\) is a constant.

We use the point (4, -6) to find \(c\):

Substitute \(x = 4\) and \(y = -6\) into the equation:

\(-6 = 2(4)^{\frac{1}{2}} - 3(4) + c\)

\(-6 = 2(2) - 12 + c\)

\(-6 = 4 - 12 + c\)

\(-6 = -8 + c\)

\(c = 2\)

Therefore, the equation of the curve is \(y = 2x^{\frac{1}{2}} - 3x + 2\).