In rectangle ABCD, we have AB\equal{}8, BC\equal{}9, H is on BC with BH\equal{}6, E is on AD with DE\equal{}4, line EC intersects line AH at G, and F is on line AD with GF⊥AF. Find the length GF.
[asy]unitsize(3mm);
defaultpen(linewidth(.8pt)+fontsize(8pt));pair D=(0,0), Ep=(4,0), A=(9,0), B=(9,8), H=(3,8), C=(0,8), G=(-6,20), F=(-6,0);draw(D--A--B--C--D--F--G--Ep);
draw(A--G);
label("F",F,W);
label("G",G,W);
label("C",C,WSW);
label("H",H,NNE);
label("6",(6,8),N);
label("B",B,NE);
label("A",A,SW);
label("E",Ep,S);
label("4",(2,0),S);
label("D",D,S);[/asy]<spanclass=′latex−bold′>(A)</span>16<spanclass=′latex−bold′>(B)</span>20<spanclass=′latex−bold′>(C)</span>24<spanclass=′latex−bold′>(D)</span>28<spanclass=′latex−bold′>(E)</span>30