Highlight cells based on the dates

I want to highlight cells based on the dates in columns D & E.


Basically, based on the dates in column D & E (which are start and finish dates), the corresponding cells from Col G onwards should be highlighted reflecting the period of the dates. So, in row 7, as the first cell is Dec-22 and greater than start Date this has to be highlighted. For, completion date, the completion is Mar-26. The period after Mar-26 is Jun-26 So, the cells from Dec-22 to Jun-26 should be highlighted.
I tried using conditional formats, but doesn't seem to work.

If the date is say Mar-26 (for Row 7) , then cell N7 should also be highlighted as it refers to period after end of Dec to end of june.

Same thing for Row 12, the Dec-27 cell should be highlighted when sep-27 is the completion date in column E (cell E11).

Any help will be appreciated.

Thanks in advance.