1. **State the problem:** We are given that $a - b = b - c = 2$ and need to find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$ 2. **Use the given equalities:** Since $a - b = 2$ and $b - c = 2$, substitute these values into the expression: $$\frac{(2)^2 + (2)^2}{(a - c)^2}$$ 3. **Simplify the numerator:** $$\frac{4 + 4}{(a - c)^2} = \frac{8}{(a - c)^2}$$ 4. **Find $a - c$:** Using the given equalities, $$a - c = (a - b) + (b - c) = 2 + 2 = 4$$ 5. **Substitute $a - c = 4$ into the denominator:** $$\frac{8}{(4)^2} = \frac{8}{16}$$ 6. **Simplify the fraction:** $$\frac{\cancel{8}}{2 \times \cancel{8}} = \frac{1}{2}$$ **Final answer:** $$\boxed{\frac{1}{2}}$$