1. The problem is to simplify the expression $\sqrt{12} - \sqrt{-4}$.\n\n2. Recall that $\sqrt{a}$ for $a \geq 0$ is the principal square root, and for negative numbers, we use imaginary numbers: $\sqrt{-b} = i\sqrt{b}$ where $b > 0$.\n\n3. Simplify $\sqrt{12}$: \n$$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}.$$\n\n4. Simplify $\sqrt{-4}$: \n$$\sqrt{-4} = i\sqrt{4} = 2i.$$\n\n5. Substitute back into the expression: \n$$2\sqrt{3} - 2i.$$\n\n6. This is the simplified form with a real part $2\sqrt{3}$ and an imaginary part $-2i$.