Given \(\frac{dy}{dx} = 2 - 8(3x + 4)^{-\frac{1}{2}}\).

When \(x = 0\), \(\frac{dy}{dx} = 2 - 8(3(0) + 4)^{-\frac{1}{2}} = 2 - 8(4)^{-\frac{1}{2}} = 2 - 8 \times \frac{1}{2} = 2 - 4 = -2\).

The rate of change of the \(x\)-coordinate is \(\frac{dx}{dt} = 0.3\).

The rate of change of the \(y\)-coordinate is given by:

\(\frac{dy}{dt} = \frac{dy}{dx} \times \frac{dx}{dt} = -2 \times 0.3 = -0.6\).

Therefore, the rate of change of the \(y\)-coordinate is 0.6 units per second.