1. **Problem:** Simplify the expression $$\sqrt{5} - 2\sqrt{6} - \sqrt{5} + 2\sqrt{6}$$. 2. **Formula and rules:** When simplifying expressions with square roots, combine like terms. Note that $$\sqrt{a} - \sqrt{a} = 0$$ and $$-2\sqrt{6} + 2\sqrt{6} = 0$$. 3. **Intermediate work:** $$\sqrt{5} - 2\sqrt{6} - \sqrt{5} + 2\sqrt{6} = (\sqrt{5} - \sqrt{5}) + (-2\sqrt{6} + 2\sqrt{6}) = 0 + 0 = 0$$ 4. **Explanation:** The terms $$\sqrt{5}$$ and $$-\sqrt{5}$$ cancel each other out, as do $$-2\sqrt{6}$$ and $$2\sqrt{6}$$, leaving zero. **Final answer:** $$0$$