1. The problem is to simplify the expression: $$21 - (6 + 3(2)) - 4(5 + 3) \div 8$$ 2. First, apply the order of operations (PEMDAS/BODMAS): parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). 3. Simplify inside the parentheses: $$6 + 3(2) = 6 + 6 = 12$$ and $$5 + 3 = 8$$ 4. Substitute back: $$21 - 12 - 4(8) \div 8$$ 5. Next, multiply and divide from left to right: $$4(8) = 32$$ So the expression becomes: $$21 - 12 - 32 \div 8$$ 6. Now divide: $$32 \div 8 = 4$$ Expression is now: $$21 - 12 - 4$$ 7. Finally, perform subtraction from left to right: $$21 - 12 = 9$$ Then: $$9 - 4 = 5$$ 8. The simplified value of the expression is: $$\boxed{5}$$