Return Count of a String Value in a Range Based on Month

[NorthbyNorthwest]

Hi, everyone. Earlier today, I asked the forum for a formula to count a specific string value in a range. Some cells in the range are empty, some contain a single string value, others multiple string values separated by a comma. The forum provided me with more than one solution. I am working with the following:

=LET(a,TRIM(TEXTSPLIT(TEXTJOIN(",",,A2:C5),,",")),ROWS(FILTER(a,a=E1&"")))

I now discover that I need the formula to count based on month. How can I amend formula so that it returns a count from range A2:C5 for the string value in cell E1 if the month in column "F" is "Oct?"

 

[NorthbyNorthwest]

I have tried using the if function. I tried using the * as you would in a sumproduct. Nothing works. I'm getting calc errors, spill errors, and other identified formula errors.

 

[NorthbyNorthwest]

Above is table. The formula returns 5 "202" values. How can I amend formula to return the 2 Oct values?