No information about the location of $E$ is given except that its distance from $D$ is $6.$ So let $E$ move all the way around the circle of radius $6$ centered at $D.$ Ask whether the distance $EF$ varies as $E$ moves along that circle. Clearly it does, but all of the specified information about the figure remains as it was; it doesn't change. Therefore the given information is not enough to say what the distance $FE$ is. But it cannot be more than $12+8+6.$