1. **Problem:** Evaluate $$\lim_{x \to 2} \frac{x^2 + 3x + 2}{x^3 + 6x}$$. 2. **Formula and rules:** To find limits of rational functions as $x$ approaches a value, substitute the value directly if the function is defined there. If substitution leads to an indeterminate form like $\frac{0}{0}$, factor and simplify. 3. **Substitute $x=2$ directly:** $$\frac{2^2 + 3(2) + 2}{2^3 + 6(2)} = \frac{4 + 6 + 2}{8 + 12} = \frac{12}{20} = \frac{3}{5}$$ 4. **Answer:** The limit is $$\boxed{\frac{3}{5}}$$. This matches option (c).