1. **State the problem:** Simplify the complex fraction $$\frac{-6 + i}{3 + 2i}$$. 2. **Formula and rule:** To simplify a fraction with complex numbers, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $$3 + 2i$$ is $$3 - 2i$$. 3. **Multiply numerator and denominator:** $$\frac{-6 + i}{3 + 2i} \times \frac{3 - 2i}{3 - 2i} = \frac{(-6 + i)(3 - 2i)}{(3 + 2i)(3 - 2i)}$$ 4. **Expand numerator:** $$(-6)(3) + (-6)(-2i) + i(3) + i(-2i) = -18 + 12i + 3i - 2i^2$$ Recall that $$i^2 = -1$$, so: $$-18 + 12i + 3i - 2(-1) = -18 + 15i + 2 = -16 + 15i$$ 5. **Expand denominator:** $$(3)^2 - (2i)^2 = 9 - 4i^2 = 9 - 4(-1) = 9 + 4 = 13$$ 6. **Write the fraction:** $$\frac{-16 + 15i}{13} = \frac{-16}{13} + \frac{15}{13}i$$ 7. **Final answer:** $$\boxed{\frac{-16}{13} + \frac{15}{13}i}$$