1. The problem is to simplify the expression $12 - \sqrt{-13}$.\n\n2. Recall that the square root of a negative number involves imaginary numbers. Specifically, $\sqrt{-a} = i\sqrt{a}$ where $i$ is the imaginary unit with the property $i^2 = -1$.\n\n3. Applying this rule, we rewrite $\sqrt{-13}$ as $i\sqrt{13}$.\n\n4. Substitute back into the expression: $$12 - \sqrt{-13} = 12 - i\sqrt{13}.$$\n\n5. This is the simplified form, expressed as a complex number with a real part 12 and an imaginary part $-\sqrt{13}$.\n\nFinal answer: $$12 - i\sqrt{13}.$$