1. The problem is to simplify the expression $(2\sqrt{3}-3)(2\sqrt{3}+3)$.\n\n2. Recognize this as a product of conjugates of the form $(a-b)(a+b) = a^2 - b^2$. Here, $a = 2\sqrt{3}$ and $b = 3$.\n\n3. Calculate $a^2 = (2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$.\n\n4. Calculate $b^2 = 3^2 = 9$.\n\n5. Substitute into the difference of squares formula: $$a^2 - b^2 = 12 - 9 = 3.$$\n\n6. Therefore, the simplified expression is $3$.