Not able to follow the narrative as the sample pic does not show B3 or B10 (?)

See if you can make something like this work. Initiate each month by the 1st day of each month ... then this formula in B2 and filled down.
Formula: copy to clipboard 
=NETWORKDAYS(EOMONTH(A2,-1)+1,EOMONTH(A2,0))



A
B
1
1st of month
workdays
2
1/1/2020
23
3
2/1/2020
20
4
3/1/2020
22
5
4/1/2020
22
6
5/1/2020
21
7
6/1/2020
22
8
7/1/2020
23
9
8/1/2020
21
10
9/1/2020
22
11
10/1/2020
22
12
11/1/2020
21
13
12/1/2020
23