1. **State the problem:** Solve for $m$ in the equation $$\frac{4}{5} = \frac{1}{8} m.$$\n\n2. **Write the formula and explain:** We want to isolate $m$ on one side. Since $m$ is multiplied by $\frac{1}{8}$, we can divide both sides by $\frac{1}{8}$ or equivalently multiply both sides by its reciprocal, 8.\n\n3. **Isolate $m$:**\n$$\frac{4}{5} = \frac{1}{8} m \implies m = \frac{4}{5} \div \frac{1}{8}.$$\n\n4. **Divide by a fraction:** Dividing by $\frac{1}{8}$ is the same as multiplying by 8, so\n$$m = \frac{4}{5} \times 8.$$\n\n5. **Simplify multiplication:**\n$$m = \frac{4 \times 8}{5} = \frac{32}{5}.$$\n\n6. **Final answer:**\n$$m = \frac{32}{5} = 6.4.$$\n\nThis means $m$ equals 6.4.