1. **Problem statement:** In triangle $\triangle ABC$, medians $AD$, $BE$, and $CF$ intersect at point $G$. Given that $AG = 6$, find the length of $GD$. 2. **Key property:** The medians of a triangle intersect at the centroid $G$, which divides each median into a ratio of $2:1$, with the longer segment adjacent to the vertex. 3. **Formula:** If $G$ is the centroid on median $AD$, then: $$AG : GD = 2 : 1$$ 4. **Calculation:** Given $AG = 6$, let $GD = x$. Then: $$\frac{AG}{GD} = \frac{2}{1} \implies \frac{6}{x} = 2 \implies x = \frac{6}{2} = 3$$ 5. **Answer:** The length of $GD$ is $3$ units.