1. Let's first understand the problem: we need to find the sum of the series $$20 - 24 + 28 - 32 + \cdots + 204 - 208$$. 2. Notice the pattern: terms alternate between positive and negative, and the numbers increase by 4 each time. 3. Label the terms as $$a_1=20, a_2=-24, a_3=28, a_4=-32, \ldots$$. 4. The absolute values form an arithmetic sequence with first term $$20$$ and common difference $$4$$. 5. Find the number of terms. The last term is either $$204$$ or $$-208$$ but since 208 appears with minus sign, the last term is $$-208$$, which means the last positive term is $$204$$. 6. Number of positive terms: starting at 20, increasing by 8 every 2 terms (since every second term is negative), so positive terms are $$20,28,36,\ldots,204$$. 7. The positive terms form an arithmetic sequence with first term $$20$$, common difference $$8$$. To find number of positive terms $$n$$ we solve: $$20 + (n-1) \times 8 = 204$$ $$8(n-1) = 184$$ $$n-1 = 23$$ $$n=24$$ positive terms. 8. Similarly, negative terms are $$-24, -32, -40, \ldots, -208$$, an arithmetic sequence with first term $$-24$$ and common difference $$-8$$. 9. Number of negative terms is also 24. 10. Total number of terms = $$24 + 24 = 48$$. 11. Sum positive terms: $$S_+ = \frac{24}{2}(20 + 204) = 12 \times 224 = 2688$$. 12. Sum negative terms: $$S_- = \frac{24}{2}(-24 + (-208)) = 12 \times (-232) = -2784$$. 13. Total sum = $$S_+ + S_- = 2688 - 2784 = -96$$. Final answer: $$\boxed{-96}$$