1. **State the problem:** Simplify the expression $$\frac{12}{4-\sqrt{3}}$$. 2. **Formula and rule:** To simplify a fraction with a radical in the denominator, multiply numerator and denominator by the conjugate of the denominator to rationalize it. The conjugate of $$4-\sqrt{3}$$ is $$4+\sqrt{3}$$. 3. **Multiply numerator and denominator by the conjugate:** $$\frac{12}{4-\sqrt{3}} \times \frac{4+\sqrt{3}}{4+\sqrt{3}} = \frac{12(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}$$ 4. **Simplify the denominator using difference of squares:** $$ (4)^2 - (\sqrt{3})^2 = 16 - 3 = 13 $$ 5. **Expand the numerator:** $$ 12 \times 4 + 12 \times \sqrt{3} = 48 + 12\sqrt{3} $$ 6. **Write the simplified fraction:** $$ \frac{48 + 12\sqrt{3}}{13} $$ 7. **Final answer:** $$ \frac{48}{13} + \frac{12}{13}\sqrt{3} $$ This is the simplified form with a rational denominator.