1. The problem is to simplify each algebraic expression by combining like terms. 2. The rule for simplifying expressions is to combine terms that have the same variable and exponent. 3. Let's simplify the first expression: $a + 2b + 2b - 4$ Combine like terms: $$a + (2b + 2b) - 4 = a + 4b - 4$$ 4. Simplify the second expression: $3a + 8a - 2b$ Combine like terms: $$3a + 8a - 2b = 11a - 2b$$ 5. Simplify the third expression: $8a + 2b + 3a - 9b$ Combine like terms: $$ (8a + 3a) + (2b - 9b) = 11a - 7b$$ 6. Simplify the fourth expression: $8a - 8 + 4a - 4b$ Combine like terms: $$ (8a + 4a) - 8 - 4b = 12a - 8 - 4b$$ 7. Simplify the fifth expression: $7a - 14b + 14 + 7b$ Combine like terms: $$7a + (-14b + 7b) + 14 = 7a - 7b + 14$$ 8. Simplify the sixth expression: $3a + 8 - 4b - 12 + 2a$ Combine like terms: $$ (3a + 2a) + (8 - 12) - 4b = 5a - 4 - 4b$$ 9. Simplify the seventh expression: $2b - 8 - 3a - 6b - 9$ Combine like terms: $$ (-3a) + (2b - 6b) + (-8 - 9) = -3a - 4b - 17$$ 10. Simplify the eighth expression: $-3a + 3b - 14a - 7b$ Combine like terms: $$ (-3a - 14a) + (3b - 7b) = -17a - 4b$$ 11. Simplify the ninth expression: $4a - 2b - 4a - 12b$ Combine like terms: $$ (4a - 4a) + (-2b - 12b) = 0 - 14b = -14b$$ 12. Simplify the tenth expression: $-6a - 4b + 2 + 3a + 12b - 6$ Combine like terms: $$ (-6a + 3a) + (-4b + 12b) + (2 - 6) = -3a + 8b - 4$$ 13. Simplify the eleventh expression: $a - 2b + 5a - 6$ Combine like terms: $$ (a + 5a) - 2b - 6 = 6a - 2b - 6$$ 14. Simplify the twelfth expression: $-15a - 3b + 16a + 4b$ Combine like terms: $$ (-15a + 16a) + (-3b + 4b) = a + b$$ 15. Simplify the thirteenth expression: $2a - 4b - 3a + 6b + 6$ Combine like terms: $$ (2a - 3a) + (-4b + 6b) + 6 = -a + 2b + 6$$ 16. Simplify the fourteenth expression: $2a + 2b - 6a - 3 - 2b + 6$ Combine like terms: $$ (2a - 6a) + (2b - 2b) + (-3 + 6) = -4a + 3$$ 17. Simplify the fifteenth expression: $3a - 6b - 6 + 2a + 6b + 2$ Combine like terms: $$ (3a + 2a) + (-6b + 6b) + (-6 + 2) = 5a - 4$$ 18. Simplify the sixteenth expression: $3a + 4a + 2b - 4 + 5b - 10$ Combine like terms: $$ (3a + 4a) + (2b + 5b) + (-4 - 10) = 7a + 7b - 14$$ Final simplified expressions: 1. $a + 4b - 4$ 2. $11a - 2b$ 3. $11a - 7b$ 4. $12a - 8 - 4b$ 5. $7a - 7b + 14$ 6. $5a - 4 - 4b$ 7. $-3a - 4b - 17$ 8. $-17a - 4b$ 9. $-14b$ 10. $-3a + 8b - 4$ 11. $6a - 2b - 6$ 12. $a + b$ 13. $-a + 2b + 6$ 14. $-4a + 3$ 15. $5a - 4$ 16. $7a + 7b - 14$