1. **Stating the problem:** Find the second derivative $f''(x)$ and the value of the third derivative at $x=2$, $f'''(2)$, for the function $$f(x) = 2x^3 - 4x^2 + 7x - 8.$$\n\n2. **Recall the rules:**\n- The first derivative $f'(x)$ is found by differentiating each term: $$\frac{d}{dx}[x^n] = nx^{n-1}.$$\n- The second derivative $f''(x)$ is the derivative of $f'(x)$.\n- The third derivative $f'''(x)$ is the derivative of $f''(x)$.\n\n3. **Find the first derivative $f'(x)$:**\n$$f'(x) = \frac{d}{dx}(2x^3) - \frac{d}{dx}(4x^2) + \frac{d}{dx}(7x) - \frac{d}{dx}(8)$$\n$$= 2 \cdot 3x^{3-1} - 4 \cdot 2x^{2-1} + 7 \cdot 1x^{1-1} - 0$$\n$$= 6x^2 - 8x + 7.$$\n\n4. **Find the second derivative $f''(x)$:**\n$$f''(x) = \frac{d}{dx}(6x^2) - \frac{d}{dx}(8x) + \frac{d}{dx}(7)$$\n$$= 6 \cdot 2x^{2-1} - 8 \cdot 1x^{1-1} + 0$$\n$$= 12x - 8.$$\n\n5. **Find the third derivative $f'''(x)$:**\n$$f'''(x) = \frac{d}{dx}(12x) - \frac{d}{dx}(8)$$\n$$= 12 - 0 = 12.$$\n\n6. **Evaluate $f'''(2)$:**\nSince $f'''(x) = 12$ is constant,\n$$f'''(2) = 12.$$\n\n**Final answers:**\n$$f''(x) = 12x - 8,$$\n$$f'''(2) = 12.$$