Geometry

Question Analysis:
This problem tests application of the diagonal bisecting property to solve for length.

Key Concept Explanation:
In all parallelograms, diagonals bisect each other at their intersection point.

Step-by-Step Solution:
Set EM = MG (bisecting property):
2y + 3 = 5y - 6
Solve for y:
3 + 6 = 5y - 2y
9 = 3y → y = 3
Find EM:
2(3) + 3 = 9
Calculate EG:
EG = EM + MG = 9 + 9 = 18