**Solution:**

To find the value of dy/dx, we need to differentiate the given function y = sin(4x + 2π/3) with respect to x.

Differentiating a function involves applying the chain rule, which states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

In this case, f(t) = sin(t) and g(x) = 4x + 2π/3. So, we need to find f'(g(x)) and g'(x) separately and then multiply them together.

**Differentiating f(t) = sin(t):**
The derivative of sin(t) with respect to t is cos(t), so f'(t) = cos(t).

**Differentiating g(x) = 4x + 2π/3:**
The derivative of 4x with respect to x is 4, as the derivative of any constant multiplied by x is the constant itself. The derivative of 2π/3 with respect to x is zero since it is a constant.

So, g'(x) = 4.

**Applying the chain rule:**
Now, we can apply the chain rule to find dy/dx.

dy/dx = f'(g(x)) * g'(x)

Substituting the values we found, we have:

dy/dx = cos(4x + 2π/3) * 4

Simplifying further, we get:

dy/dx = 4cos(4x + 2π/3)

Therefore, the value of dy/dx is 4cos(4x + 2π/3).

In conclusion, the derivative of y = sin(4x + 2π/3) with respect to x is dy/dx = 4cos(4x + 2π/3).