1. **Problem:** Find the domain of definition of the function $$f(x)=\frac{x^2 - x + 6}{2x - 8}$$. 2. **Formula and rules:** The domain of a rational function is all real numbers except where the denominator is zero. 3. **Work:** Set denominator equal to zero: $$2x - 8 = 0$$ $$2x = 8$$ $$x = 4$$ 4. **Conclusion:** The domain is all real numbers except $$x = 4$$. **Final answer:** $$\boxed{\{x \in \mathbb{R} : x \neq 4\}}$$