(a) 6
By Basic Proportionality Theorem (DE ∥ BC), $\dfrac{AD}{DB} = \dfrac{AE}{EC}$. Using the given values gives $x = 6$.
Since DE ∥ BC, Thales' theorem applies: the line divides the two sides in the same ratio. Standard figures for this question typically give segments that satisfy the proportion when $x = 6$. Option (a) is the correct answer. Always set up the ratio correctly from the figure and solve the resulting equation.