1. **State the problem:** Solve for $z$ in the equation $$\frac{z}{12} = \frac{4}{5}.$$\n\n2. **Formula and rules:** To solve for $z$, we use the property of equality of fractions: if $$\frac{a}{b} = \frac{c}{d},$$ then $$a \times d = b \times c.$$\n\n3. **Apply the cross multiplication:** $$z \times 5 = 12 \times 4.$$\n\n4. **Calculate the right side:** $$z \times 5 = 48.$$\n\n5. **Isolate $z$ by dividing both sides by 5:** $$z = \frac{48}{5}.$$\n\n6. **Show cancellation step:** $$z = \frac{\cancel{48}}{\cancel{5}}$$ (no common factors to cancel here, so fraction remains as is).\n\n7. **Final answer:** $$z = \frac{48}{5} = 9.6.$$