The image shows a triangle and related mathematical information. To analyze and solve the problem fully, I need to extract the provided details, such as triangle dimensions and other relevant equations.

Details extracted from the image:

• A triangle labeled $\triangle ABC$, where the lengths are provided:
  • $BD = 6$ (likely in the unit specified, such as cm or units)
  • $AC = 4$
  • $BC = ?$ (this is the unknown value we need to solve for)

The problem also specifies a condition involving relationships or geometric properties (possibly trigonometry, Pythagorean theorem, or proportionality).

Would you like me to analyze it assuming it involves the Pythagorean theorem (if it's a right triangle) or other geometric principles? Let me know!