I'm not certain how large a spanner the merged cells (and the variety in the number of cells that were merged) will throw into the works here.
You could try:
Entering the starting dates ( 13.09 and 16.09 ) in cells D1 and F1, then checking to see if Numbers recognized them as Day and Month of a Date and Time value.
If not (which I suspect will be the case), try a different separator, or create a custom format for Date and Time values to match the format you want.
Once you have a working format, recognized as a D&T value, try this:
Select the cell containing for 13.09 (expressed in the format you created or chose), then hover toe pointer near the bottom edge of that cell. When a yellow dot appears at the centre of the bottom boundary of the cell, clck and hold on it, then drag down to fill the incremented values into the cells below.
IF the dates increment by one day in each cell, you have a method of filling the dates into the cells as needed. Try it a second time on the date in the adjacent table starting with 16.09.
If it works with the different sized merged cells, try selecting both cells containing dates in row 1 of the next table to determine whethet you can simultaneously fill into both columns, despite the different sizes of the cells in each column. (This will likely NOT work if these are two different tables, and not a single table with the cell top and bottom boundaries hidden in a column between the two columns containing D&T values.)
If filling the dates in using this method does not work, you could try using a formula.
Enter the initial date in each column, then in the next (merged) cell of column D enter the formula: D1 + "1d"
and fill down as before. Repeat with the date in column F, and note particularly, the result in the last cell of that column as displayed in your example.
As a general recommendation, I'd suggest NOT using merged cells where they can b avoided. Some of the side effects are loss of the ability to sort the table and loss of the ability to filter the table.
Regards,
Barry