1. The problem asks for the phase shift of the function $$y = 4\cos\left(\frac{1}{2}x + \pi\right) - 2$$. 2. The general form of a cosine function with phase shift is $$y = A\cos(B(x - C)) + D$$, where $C$ is the phase shift. 3. We need to rewrite the inside of the cosine to match the form $B(x - C)$: $$\frac{1}{2}x + \pi = \frac{1}{2}\left(x + 2\pi\right)$$ 4. From this, we identify $B = \frac{1}{2}$ and the expression inside the parentheses is $x - (-2\pi)$, so the phase shift $C = -2\pi$. 5. The phase shift is calculated as $$\text{Phase shift} = \frac{-\text{constant term inside}}{B} = \frac{-\pi}{\frac{1}{2}} = -2\pi$$. 6. A negative phase shift means the graph shifts to the left by $2\pi$. 7. Among the answer options, $2\pi$ is listed (without sign), so the phase shift magnitude is $2\pi$ to the left. Final answer: The phase shift is $2\pi$ to the left.