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Default Average with multiple conditions

I'm trying to calcluate the average where multiple conditions have to be met.
I've tried a couple of different formulas based on other postings, but I
continue to get "0".

I'm trying to calculate the average of months open (Column F) if the
following conditions apply:
Date closed is = A1
Date closed <=B1
Bucket = "12 Month"

Column D Column E Column F
Date Closed Bucket Months Open
1/5/2006 12 Month 11.2
1/1/2004 24 Month 16
2/1/2006 48 Month 52
2/5/2006 12 Month 6.1
1/5/2004 24 Month 27
2/1/2004 48 Month 60

I've tried the following formula, but I get a value of 0:
=if(a1=0,0,average(if(D1:D6<=A1,if(D1:D6<=B1,if(E1 :E6="12 Month", F1:F6)))))


 
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