We have two triangles, $\triangle ABC$ and $\triangle DEF$, and the following conditions:

• $AB \cong DE$ (Side $AB$ is congruent to side $DE$)
• $AC \cong DF$ (Side $AC$ is congruent to side $DF$)
• $\angle CAB \cong \angle FDE$ (Angle $CAB$ is congruent to angle $FDE$)

Given these conditions, we can conclude that the two triangles are congruent by the Side-Angle-Side (SAS) criterion. According to SAS, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Since the triangles are congruent, the corresponding sides are also congruent. Therefore, the side $BC$ in $\triangle ABC$ will be congruent to the side $EF$ in $\triangle DEF$.

The problem tells us that the length of side $BC$ is $x - 4$. So, the corresponding side $EF$ in $\triangle DEF$ will also have length $x - 4$. If we had the length of side $EF$, we could solve for $x$.

However, to fully solve for $x$, we need more information, such as the length of side $EF$ or additional relationships between the two triangles. Do you have that information or additional conditions?

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Would you like more details on how SAS works, or is there more information available? Let me know if you want to continue solving!

Here are some additional related questions:

1. How do we use the congruence of triangles to find unknown side lengths?
2. What is the significance of the SAS congruence criterion in triangle geometry?
3. How do we solve for variables in geometric problems?
4. What are the other triangle congruence criteria besides SAS?
5. How do we apply triangle similarity in solving geometric problems?

Tip: Always check if additional information (like side lengths or angles) is provided when dealing with congruent triangles, as it helps in solving for unknowns.