Extracting information based on mutliple criteria and date range

I've been working on this equation for a few days now to extract information based on matching criteria within a date range. A couple of formulas I've tried are index/match and sumifs but cant get either to work. So here is what I have, in columns B and C are my date ranges, column D is the product and E is the TPH. Then in column H I have my product I'm trying to match based on the date ranges by month in Row 2 going across. What I'd like to do is publish the TPH that corresponds with the product and the month it's located in I2:T10 (highlighted section).

This is based on FROM date:

in I3

=IFERROR(INDEX($E$2:$E$41,MATCH(1,($H3=$D$2:$D$41)*(I$2=$B$2:$B$41),0)),"")

Enter with Ctrl+Shift+Enter

Copy down and across

Thanks for the quick response but when I enter the formula it only displays the TPHs that begin with the From date. Are there any other ways that it can see the date in Row 2 and distinguish if it falls between the date range in columns B and C?

Try

=IFERROR(INDEX($E$2:$E$41,MATCH(1,($H3=$D$2:$D$41)*(I$2>=$B$2:$B$41)*(I$2<=$C$2:$C$41),0)),"")

Enter with Ctrl+Shift+Enter (as before)

This check for dates >= to B dates and <= to C Dates