In the figure, ∠EAB and ∠ABC are right angles. AB \equal{} 4, BC \equal{} 6, AE \equal{} 8, and AC and BE intersect at D. What is the difference between the areas of △ADE and △BDC?
[asy]unitsize(4mm);
defaultpen(linewidth(.8pt)+fontsize(10pt));pair A=(0,0), B=(4,0), C=(4,6), Ep=(0,8);
pair D=extension(A,C,Ep,B);draw(A--C--B--A--Ep--B);
label("A",A,SW);
label("B",B,SE);
label("C",C,N);
label("E",Ep,N);
label("D",D,2.5*N);
label("4",midpoint(A--B),S);
label("6",midpoint(B--C),E);
label("8",(0,3),W);[/asy]<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>9