1. **Restate the question:** You asked how we found the value 4 for the denominator in the expression $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$. 2. **Recall the relationship:** We know that $$a - b = 2$$ and $$b - c = 2$$. 3. **Find $$a - c$$:** Since $$a - c = (a - b) + (b - c)$$, we add the two known differences: $$a - c = 2 + 2 = 4$$ 4. **Why add?** Because subtracting $$c$$ from $$a$$ is the same as subtracting $$b$$ from $$a$$ and then subtracting $$c$$ from $$b$$, so the differences add up. 5. **Therefore, the denominator is:** $$(a - c)^2 = 4^2 = 16$$ This is why the denominator is 4 squared, or 16, in the original expression.