Given the curve equation \(y = x^2 - 2x - 3\), we need to find \(\frac{dy}{dx}\).

Differentiate \(y\) with respect to \(x\):

\(\frac{dy}{dx} = 2x - 2\).

We know \(\frac{dy}{dt} = 4\) and \(\frac{dx}{dt} = 6\).

Using the chain rule, \(\frac{dy}{dt} = \frac{dy}{dx} \cdot \frac{dx}{dt}\).

Substitute the known values:

\(4 = (2x - 2) \cdot 6\).

Solve for \(x\):

\(4 = 12x - 12\)

\(16 = 12x\)

\(x = \frac{16}{12} = \frac{4}{3}\).