This problem appears to be a geometry question written in Sinhala that involves a quadrilateral $ABCD$ and some conditions on the sides and diagonals. Let me translate and break it down:

Translation (Overview):

• $ABCD$ is a quadrilateral.
• $AB = 6a$, $BC = 8a$, and various other sides and diagonals are mentioned.
• The forces along these sides are given as $12P, 3P, 4P, 3P, 15P$, which likely correspond to the sides or diagonals of the quadrilateral.
• It discusses the concept of equilibrium and finding an unknown point $G$, possibly the center of mass or some geometric point.

Based on the structure of the problem, it seems to involve vector equilibrium or force balance in a quadrilateral. The values given suggest that you need to solve for unknown distances or use the properties of vectors to determine a geometric relationship.

Do you want a more detailed step-by-step breakdown of how to approach solving this? I can also provide clarifications on specific parts of the problem if needed.