1. **State the problem:** Solve for the exact value of $x$ in the equation $$3 \ln(6x + 8) - 12 = -18.$$\n\n2. **Isolate the logarithmic term:** Add 12 to both sides to get $$3 \ln(6x + 8) = -18 + 12 = -6.$$\n\n3. **Divide both sides by 3:** $$\ln(6x + 8) = \frac{-6}{3} = -2.$$\n\n4. **Rewrite the logarithmic equation in exponential form:** Recall that if $\ln(a) = b$, then $a = e^b$. So, $$6x + 8 = e^{-2}.$$\n\n5. **Solve for $x$:** Subtract 8 from both sides: $$6x = e^{-2} - 8.$$ Then divide both sides by 6: $$x = \frac{e^{-2} - 8}{6}.$$\n\n6. **Final answer:** $$\boxed{x = \frac{e^{-2} - 8}{6}}.$$