1. **State the problem:** Solve the proportion equation $$\frac{8}{v-4} = \frac{4}{3}$$ for $v$. 2. **Use the cross-multiplication rule:** For proportions of the form $$\frac{A}{B} = \frac{C}{D}$$, cross-multiply to get $$A \times D = B \times C$$. 3. **Apply cross-multiplication:** $$8 \times 3 = (v-4) \times 4$$ 4. **Simplify both sides:** $$24 = 4(v-4)$$ 5. **Distribute 4 on the right side:** $$24 = 4v - 16$$ 6. **Add 16 to both sides to isolate terms with $v$:** $$24 + 16 = 4v - 16 + 16$$ $$40 = 4v$$ 7. **Divide both sides by 4 to solve for $v$:** $$\frac{40}{\cancel{4}} = \frac{4v}{\cancel{4}}$$ $$10 = v$$ **Final answer:** $$v = 10$$