1. **State the problem:** Solve the proportion $$\frac{v - 4}{8} = \frac{4}{3}$$ for $v$. 2. **Formula and rule:** To solve a proportion $$\frac{A}{B} = \frac{C}{D}$$, cross-multiply to get $$A \times D = B \times C$$. 3. **Apply cross-multiplication:** $$ (v - 4) \times 3 = 8 \times 4 $$ 4. **Simplify both sides:** $$ 3(v - 4) = 32 $$ 5. **Distribute 3:** $$ 3v - 12 = 32 $$ 6. **Add 12 to both sides:** $$ 3v - 12 + 12 = 32 + 12 $$ $$ 3v = 44 $$ 7. **Divide both sides by 3:** $$ \frac{\cancel{3}v}{\cancel{3}} = \frac{44}{3} $$ $$ v = \frac{44}{3} $$ 8. **Final answer:** $$ v = \frac{44}{3} $$ or approximately 14.67. This is the simplified solution for $v$ in the given proportion.