1. **State the problem:** Solve the equation $$(2 - 3\ln)^{\frac{4}{3}} = 256$$ for $\ln$. 2. **Rewrite the equation:** Recognize that 256 is a power of 4, since $$256 = 4^4$$. 3. **Set the bases equal:** Since the left side is raised to the power $\frac{4}{3}$, we can write $$\left(2 - 3\ln\right)^{\frac{4}{3}} = 4^4$$ 4. **Take both sides to the power $\frac{3}{4}$ to isolate the base:** $$\left(\left(2 - 3\ln\right)^{\frac{4}{3}}\right)^{\frac{3}{4}} = \left(4^4\right)^{\frac{3}{4}}$$ 5. **Simplify the exponents:** $$2 - 3\ln = 4^{4 \times \frac{3}{4}} = 4^3 = 64$$ 6. **Solve for $\ln$:** $$2 - 3\ln = 64$$ $$-3\ln = 64 - 2$$ $$-3\ln = 62$$ 7. **Divide both sides by $-3$:** $$\ln = \frac{62}{-3} = -\frac{62}{3}$$ **Final answer:** $$\boxed{\ln = -\frac{62}{3}}$$