1. **State the problem:** Simplify the expression $21 - (-2x - 8)$. 2. **Recall the rule:** Subtracting a negative expression is equivalent to adding its opposite. So, $a - (-b) = a + b$. 3. **Apply the rule:** $$21 - (-2x - 8) = 21 + (2x + 8)$$ 4. **Remove parentheses:** $$21 + 2x + 8$$ 5. **Combine like terms:** $$21 + 8 = 29$$ 6. **Final simplified expression:** $$29 + 2x$$