1. **State the problem:** Solve the equation $$6 + \frac{4}{5}b = \frac{9}{10}b$$ for the variable $b$. 2. **Write down the formula and rules:** We want to isolate $b$ on one side. To do this, we will move all terms involving $b$ to one side and constants to the other. 3. **Subtract $\frac{4}{5}b$ from both sides:** $$6 + \frac{4}{5}b - \frac{4}{5}b = \frac{9}{10}b - \frac{4}{5}b$$ which simplifies to $$6 = \frac{9}{10}b - \frac{4}{5}b$$ 4. **Find a common denominator to combine the $b$ terms:** $$\frac{4}{5}b = \frac{8}{10}b$$ so $$6 = \frac{9}{10}b - \frac{8}{10}b = \left(\frac{9}{10} - \frac{8}{10}\right)b = \frac{1}{10}b$$ 5. **Solve for $b$ by dividing both sides by $\frac{1}{10}$:** $$b = \frac{6}{\frac{1}{10}}$$ 6. **Use the cancellation notation:** $$b = 6 \times \cancel{\frac{1}{\frac{1}{10}}} = 6 \times 10 = 60$$ 7. **Final answer:** $$\boxed{60}$$ This means the value of $b$ that satisfies the equation is 60.