Note that the decrease from FD to GH is proportional to the decrease from ED to EG.
Since GH is 1/2 of FD(6 is 1/2 of 12), we can deduce that EG is 1/2 of GD:
1/2(ED) = EG
1/2((x+5)+9) = x+5
1/2(x+14) = x + 5
x + 14= 2x + 10
4 = x
Since HF is also 9, we can apply the same logic to EH, meaning that EH = x+5
EH = x + 5
EH = (4) + 5
EH = 9