Hello everyone!
Why can not I change the color part of date or the number?

I don't have the slightest idea what you mean.

I have the date in the cell: 12.06.2016. How do I change color only part of the date? To date was as follows: 12.06.2016. But this type of data was date.

When I enter a date I do it as: dd-mm-yyyy
Entered that way I can't format individual part of the date. If I change it to text by entering 'dd-mm-yyyy I can format mm with red color (highlight mm and select red font color).

You may be able to do the same if you enter '12.06.2016

If 12.06.2016 is entered as date or generated by formula you can't format part of the date.