连接BF,
∵AD=DB,DF⊥AB,∠ACB=90
∴AF=BF,∠AFD=∠BFD,CD=AD=BD=6
又∵∠ABC+∠A=90,∠AFD+∠A=90
∴∠ABC=∠AFD
∴∠ABC=∠BFD
∴RT△BDE≈RT△FDB
∴DB/DE=DF/DB,即
6/4=DF/6
DF=9