1. **State the problem:** Solve the equation $$\frac{12}{b} - 3 = \frac{6}{b} + 4$$ for $b$. 2. **Isolate terms with $b$:** Move all terms involving $b$ to one side and constants to the other: $$\frac{12}{b} - \frac{6}{b} = 4 + 3$$ 3. **Combine like terms:** $$\frac{12 - 6}{b} = 7$$ $$\frac{6}{b} = 7$$ 4. **Solve for $b$:** Multiply both sides by $b$ and divide both sides by 7: $$6 = 7b$$ $$b = \frac{6}{7}$$ 5. **Check the answer:** Substitute $b = \frac{6}{7}$ back into the original equation to verify correctness. **Final answer:** $b = \frac{6}{7}$