working days and quarters

Hello dear Community,

I am kindly asking you experts to help me with this case : I have 2 given dates ( start , end ) and a correction factor (utilization) .
I want to calculate how many working days are in each month between the given dates * utilization; and same thing per quarters .

I attached a file for a better understanding.

thank you so much and I am eager for a solution.

have a nice day