1. **State the problem:** Solve the equation $$\frac{6}{3} = \frac{V + 11}{3V - 12}$$ for $V$. 2. **Simplify the left side:** $$\frac{6}{3} = 2$$, so the equation becomes $$2 = \frac{V + 11}{3V - 12}$$. 3. **Use cross multiplication:** Multiply both sides by $3V - 12$ to eliminate the denominator: $$2(3V - 12) = V + 11$$. 4. **Expand the left side:** $$6V - 24 = V + 11$$. 5. **Bring all terms involving $V$ to one side and constants to the other:** $$6V - V = 11 + 24$$ $$5V = 35$$. 6. **Divide both sides by 5 to solve for $V$:** $$\frac{\cancel{5}V}{\cancel{5}} = \frac{35}{5}$$ $$V = 7$$. **Final answer:** $$V = 7$$.