In a 30-60-90 triangle, the side lengths are in the ratio of \(1:\sqrt{3}:2\). Specifically:
- The shorter leg (opposite the 30-degree angle) is \(x\).
- The longer leg (opposite the 60-degree angle) is \(x\sqrt{3}\).
- The hypotenuse (opposite the right angle) is \(2x\).
Given that the hypotenuse is 12, we can set up the equation:
\[ 2x = 12 \]
Solving for \(x\):
\[ x = \frac{12}{2} = 6 \]
Now, the length of the longer leg is:
\[ x\sqrt{3} = 6\sqrt{3} \]
So, the length of the longer leg is \(6\sqrt{3}\).
Among the options provided, the correct response is \(6\sqrt{3}\).