Finding the area of a triangle

By Ceva's Theorem .

$\dfrac{AF}{FB} \times \dfrac{BD}{DC} \times \dfrac{CE}{EA} = 1$

By the Angle Bisector Theorem .

$\dfrac{BD}{DC}=\dfrac{AB}{AC}=\dfrac{4}{6}$

Since $BE$ is a median,

$\dfrac{CE}{EA}=1$

Substituting, we get

$\dfrac{AF}{4-AF} \times \dfrac{4}{6} \times 1 = 1$

$\dfrac{4AF}{24-6AF}=1$

$4AF=24-6AF$

$10AF=24$

$AF=\dfrac{24}{10}=$ $\boxed{2.4}$