1. **State the problem:** Simplify the expression $$\frac{12}{2 - \sqrt{3}}$$. 2. **Formula and rule:** To simplify expressions with radicals in the denominator, multiply numerator and denominator by the conjugate of the denominator to rationalize it. 3. **Identify the conjugate:** The conjugate of $2 - \sqrt{3}$ is $2 + \sqrt{3}$. 4. **Multiply numerator and denominator by the conjugate:** $$\frac{12}{2 - \sqrt{3}} \times \frac{2 + \sqrt{3}}{2 + \sqrt{3}} = \frac{12(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}$$ 5. **Simplify the denominator using difference of squares:** $$ (2)^2 - (\sqrt{3})^2 = 4 - 3 = 1 $$ 6. **Substitute back:** $$ \frac{12(2 + \sqrt{3})}{1} = 12(2 + \sqrt{3}) $$ 7. **Distribute 12:** $$ 12 \times 2 + 12 \times \sqrt{3} = 24 + 12\sqrt{3} $$ **Final answer:** $$24 + 12\sqrt{3}$$