Answer
$EC=12$
Work Step by Step
The parallel line that crosses through the triangle creates proportional sides in the triangle. Or, in other words...
$\frac {AD}{DB}=\frac {AE}{EC}$
Substitute in known values, and $x$ for the unknown value...
$\frac{6}{8}=\frac{9}{x}$
Cross Multiply...
$6x=8(9)$
$6x=72$
Divide both sides by six...
$x=12$ or $EC=12$
