1. The problem asks to find the domain of the function $$y = 2 (x - 3)^2 - 4$$. 2. The function is a quadratic in the form of $$y = a(x-h)^2 + k$$, where $$a=2$$, $$h=3$$, and $$k=-4$$. 3. Since it is a polynomial function (quadratic), it is defined for all real values of $$x$$. 4. Therefore, the domain is all real numbers, written as $$\{x \mid x \in \mathbb{R} \}$$. 5. Among the choices given, this corresponds to Answer B: $$\{x \mid x \in \mathbb{R} \}$$. Final answer: The domain of $$y = 2 (x - 3)^2 - 4$$ is $$\boxed{\{x \mid x \in \mathbb{R} \}}$$.