Correct Answer: $2 \sqrt{3}$ cm

Solution :
Given: $\triangle ABC$ is an equilateral triangle with a side of 12 cm and AD is the median.
Use the formula,
The height of the equilateral triangle = $\frac{\sqrt3}{2}\times x$ where $x$ is its side.
Also, the centroid divides the median in the ratio of 2 : 1.
The height of the equilateral triangle = $\frac{\sqrt3}{2}\times 12$.
⇒ AD = $6\sqrt3$ cm
Also, AG : GD = 2 : 1
Let AG be $2x$.
⇒ GD = $x$, AD = $3x$
The length of GD is given as,
⇒ $3x=6\sqrt 3$
⇒ $x=2\sqrt 3$ cm
⇒$GD=2\sqrt 3$ cm
Hence, the correct answer is $2 \sqrt{3}$ cm.