1. **State the problem:** Find the limit $$\lim_{x \to 2} (8 - 3x + 12x^2)$$. 2. **Recall the limit rule for polynomials:** The limit of a polynomial function as $x$ approaches a value is simply the value of the polynomial evaluated at that point. 3. **Evaluate the polynomial at $x=2$:** $$8 - 3(2) + 12(2)^2 = 8 - 6 + 12 \times 4$$ 4. **Calculate step-by-step:** $$8 - 6 + 48 = 2 + 48 = 50$$ 5. **Conclusion:** The limit is $$\boxed{50}$$ because the polynomial is continuous everywhere, so direct substitution works.