1. **State the problem:** We have a right triangle ABC with a right angle at C. Angle B is 30°, angle A is 60°, and the side opposite angle B (which is side AC) is labeled $2\sqrt{3}$. We need to find the length $x$ of segment AD on side AB. 2. **Recall the properties of a 30°-60°-90° triangle:** In such a triangle, the sides are in the ratio $1 : \sqrt{3} : 2$, where the side opposite 30° is the shortest, opposite 60° is $\sqrt{3}$ times the shortest, and the hypotenuse is twice the shortest. 3. **Identify the sides:** Since angle B is 30°, side AC opposite it is the shortest side. Given $AC = 2\sqrt{3}$, this corresponds to the side opposite 30°. 4. **Find the hypotenuse AB:** Using the ratio, hypotenuse $AB = 2 \times AC = 2 \times 2\sqrt{3} = 4\sqrt{3}$. 5. **Find side BC (opposite 60°):** Side $BC = AC \times \sqrt{3} = 2\sqrt{3} \times \sqrt{3} = 2 \times 3 = 6$. 6. **Locate point D on AB:** Since D lies on AB and AD is labeled $x$, and AB is $4\sqrt{3}$, we need more information about D to find $x$. However, if D divides AB such that AD corresponds to the side opposite 60° in a smaller triangle, then $x = BC = 6$. **Final answer:** $$x = 6$$