1. **State the problem:** Simplify the linear equation $$-12 - 4c - 16a = -6c - 19a + 2 + 2b$$. 2. **Rewrite the equation:** Move all terms to one side to combine like terms. 3. **Add $6c$ to both sides:** $$-12 - 4c + 6c - 16a = -19a + 2 + 2b$$ simplifies to $$-12 + 2c - 16a = -19a + 2 + 2b$$. 4. **Add $19a$ to both sides:** $$-12 + 2c - 16a + 19a = 2 + 2b$$ simplifies to $$-12 + 2c + 3a = 2 + 2b$$. 5. **Subtract 2 from both sides:** $$-12 + 2c + 3a - 2 = 2 + 2b - 2$$ simplifies to $$-14 + 2c + 3a = 2b$$. 6. **Rewrite the equation:** $$2c + 3a - 14 = 2b$$. 7. **Isolate $b$ by dividing both sides by 2:** $$b = \frac{2c + 3a - 14}{2}$$. **Final simplified form:** $$b = \frac{2c + 3a - 14}{2}$$.