1. **State the problem:** Solve the equation $2(4x+3)+4=-2(-4x-6)-2$ using the river method. 2. **Distribute the constants:** $$2 \times 4x = 8x, \quad 2 \times 3 = 6$$ $$-2 \times -4x = 8x, \quad -2 \times -6 = 12$$ So the equation becomes: $$8x + 6 + 4 = 8x + 12 - 2$$ 3. **Simplify both sides:** $$8x + 10 = 8x + 10$$ 4. **Apply the river method:** The river method involves moving all terms with $x$ to one side and constants to the other side by adding or subtracting terms across the equals sign. Subtract $8x$ from both sides: $$8x + 10 - \cancel{8x} = 8x + 10 - \cancel{8x}$$ which simplifies to: $$10 = 10$$ 5. **Interpret the result:** Since the variables cancel out and we get a true statement $10=10$, the equation is an identity. **Final answer:** The equation is true for all real values of $x$. There are infinitely many solutions.