We are given a triangle ACE.

Step 1: Analyze the given information and diagram.
We are given a triangle $\triangle ACE$.

• $BF \parallel CE$.
• $BC = \frac{3}{8} AC$.
• $AE : ED = 4 : 3$.
• We need to determine the ratio $DG : GB$.

From the diagram, $G$ is the intersection of lines $BD$ and $CE$.
The line $CGE$ is a transversal intersecting the sides of $\triangle ABD$.
The vertices of $\triangle ABD$ are $A$, $B$, $D$.
The transversal $CGE$ intersects:

• Side $AB$ at point $B$ (extended, as $C$ is on the line containing $AB$).
• Side