1. **Problem:** Find the limit of $$\frac{6x^2 - 17x + 12}{2x^2 - x - 3}$$ as $$x \to 4$$. 2. **Formula:** For polynomial limits at a point, substitute the value directly if the denominator is not zero. 3. **Step 1:** Substitute $$x=4$$ into numerator: $$6(4)^2 - 17(4) + 12 = 6 \times 16 - 68 + 12 = 96 - 68 + 12 = 40$$ 4. **Step 2:** Substitute $$x=4$$ into denominator: $$2(4)^2 - 4 - 3 = 2 \times 16 - 4 - 3 = 32 - 4 - 3 = 25$$ 5. **Step 3:** Calculate the limit: $$\frac{40}{25} = \frac{8}{5} = 1.6$$ **Final answer:** $$\boxed{\frac{8}{5}}$$