Question

In triangle ABC, medians AD, BF, and CE intersect at G. What is the length of GE is CH=12?

Answer 1

You do not have any point labeled "H" in your diagram.

What I can tell you is that point "G" (where all 3 medians meet) is called a centroid.

Along each median:
the distance from EACH vertex to the centroid (point G) is TWICE the distance from the centroid to the side.
CG = 2*GE   AG = 2*GD   BG = 2*GF