1. **State the problem:** Solve for $v$ in the equation $\frac{v}{9} = \frac{8}{12}$.\n\n2. **Use the cross-multiplication method:** For equations of the form $\frac{a}{b} = \frac{c}{d}$, cross-multiply to get $a \times d = b \times c$.\n\n3. **Apply cross-multiplication:** Multiply both sides: $v \times 12 = 9 \times 8$.\n\n4. **Calculate the products:** $12v = 72$.\n\n5. **Solve for $v$:** Divide both sides by 12 to isolate $v$: $v = \frac{72}{12}$.\n\n6. **Simplify the fraction:** $v = 6$.\n\n**Final answer:** $v = 6$.