In a 30-60-90 triangle, the lengths of the sides are in a specific ratio:
- The side opposite the 30-degree angle is \( x \).
- The side opposite the 60-degree angle is \( x\sqrt{3} \).
- The hypotenuse is \( 2x \).
Given that the side opposite the 60-degree angle is \( 6\sqrt{3} \), we have:
\[ x\sqrt{3} = 6\sqrt{3} \]
To find \( x \), we can divide both sides by \( \sqrt{3} \):
\[ x = 6 \]
Now that we have \( x \), we can determine the length of the hypotenuse:
\[ \text{Hypotenuse} = 2x = 2 \times 6 = 12 \]
Therefore, the length of the hypotenuse is \( \boxed{12} \).