Let's analyze the wave equation step by step.

The given wave is:

$$y(x, t) = 4.0 \sin \left[20 \times 10^{-3} x + 600 t\right] \text{ mm}.$$

First, simplify the coefficient of $ x $:

$$20 \times 10^{-3} = 0.02 \, \text{mm}^{-1}.$$

So the equation becomes:

$$y(x, t) = 4.0 \sin\left(0.02x + 600t\right) \text{ mm}.$$

A standard form for a travelling wave is:

$$y(x, t) = A \sin(kx - \omega t)$$

which represents a wave moving in the positive $ x $-direction with speed $ v = \frac{\omega}{k} $.

Notice that our wave equation has the form:

$$\sin(0.02x + 600t)$$

The positive sign in front of $ 600t $ means we can rewrite the phase as:

$$0.02x + 600t = 0.02x - (-600t),$$

which indicates that the angular frequency $ \omega $ in the standard form is effectively $ -600 $.

The velocity $ v $ of a wave is determined from the phase (for a constant phase, $ \phi = $ constant):

$$k x + \omega t = \text{constant}.$$

Differentiating with respect to $ t $:

$$k \frac{dx}{dt} + \omega = 0,$$

which gives:

$$\frac{dx}{dt} = -\frac{\omega}{k}.$$

Substituting the values:

$ k = 0.02 \, \text{mm}^{-1} $

$ \omega = 600 \, \text{s}^{-1} $

We have:

$$v = -\frac{600}{0.02} = -30000 \text{ mm/s}.$$

Convert the velocity from mm/s to m/s:

$$-30000 \, \text{mm/s} = -30 \, \text{m/s}.$$

Thus, the velocity of the wave is $-30 \, \text{m/s}$.

The correct answer is Option D.