To simplify $\frac{12}{2\sqrt{3} + 3}$, we need to rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator, which is $2\sqrt{3} - 3$.

$\frac{12}{2\sqrt{3} + 3} \times \frac{2\sqrt{3} - 3}{2\sqrt{3} - 3} = \frac{12(2\sqrt{3} - 3)}{(2\sqrt{3} + 3)(2\sqrt{3} - 3)}$

The denominator becomes: $(2\sqrt{3} + 3)(2\sqrt{3} - 3) = (2\sqrt{3})^2 - 3^2 = 4 \times 3 - 9 = 12 - 9 = 3$

The numerator becomes: $12(2\sqrt{3} - 3) = 24\sqrt{3} - 36$

Thus, the fraction simplifies to: $\frac{24\sqrt{3} - 36}{3} = 8\sqrt{3} - 12$

Factoring out the greatest common factor of 4: $4(2\sqrt{3} - 3)$

So, the simplified form is option d. $4(2\sqrt{3} - 3)$.