1. Stating the problem: Simplify the algebraic expression $$-8x - 12 - 4x - 24x + 12 - a - 3b - 7a + b + 6$$. 2. Group like terms: Combine terms with $x$, constants, $a$, and $b$ separately. 3. Combine $x$ terms: $$-8x - 4x - 24x = (-8 - 4 - 24)x = -36x$$. 4. Combine constants: $$-12 + 12 + 6 = 6$$. 5. Combine $a$ terms: $$-a - 7a = -8a$$. 6. Combine $b$ terms: $$-3b + b = -2b$$. 7. Write the simplified expression: $$-36x + 6 - 8a - 2b$$. This is the fully simplified form of the given expression.