count number of times a text appeared in a month in given range of dates and names

Hi,
In sheet1 I have date in column 'A' & 'H' and names in column 'B' & 'I'

In sheet2 I have month ( Jan to Dec) in column 'A' and in columns B to J are the Names.
I am trying to count in sheet2 how many times that the name has appeared in particular month in sheet1 in the columns given.

If any one can help please
sample file is attached

Kind regards

I am trying the following

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Hi PCI,
Thanks for your help. It looks good, however:
Jan gives value of 2 for name 'Make' where as it is only once
Feb 'Sake' appears once in the list but shows as zero.
Any further help please
Kind regards

Did you check the data in the file sent: I modified some values for debugging
Make appears twice in Jan
Fake appears for June only

Hi,
Apology. Cant seem to understand.
I have checked the modified sheet.
Please have a look . I have attached it again.
Thanks
kind regards

Hi PCI,
I have figured it out now.
You were right.
It is a great help from you.
I have clicked * to express my gratitude.
Really thanks
Kind regards

As I explained the formula is only for the first bank of data.
The complete formula is:
B2 =SUMPRODUCT((MONTH(Sheet1!$A$2:$A$21) = VLOOKUP($A2,MonthList,2,0))*(Sheet1!$B$2:$B$21=B$1))+SUMPRODUCT((MONTH(Sheet1!$H$2:$H$21) = VLOOKUP($A2,MonthList,2,0))*(Sheet1!$I$2:$I$21=B$1))

"It is a great help from you.
I have clicked * to express my gratitude.
Really thanks
Kind regards"

You're welcome, thank you for the thanks back
PCI