usually field status in HP PPM depends on the request status. In the workbench, you can look for the request type "Change Request" (or whatever this is called on your instance), open it and go to the "Status Dependencies" tab. Let's say the status your particular change request is in is called "Work in Progress". Then you click on "Work in Progress" in the left list and then look for your field "Date of Implementation" on the right. Mark "Editable" and click "Save". Now you can change "Date of Implementation" for all requests of type "Change Request" in status "Work in Progress".
If you just want to change the one date, go into the change request form in the HTML interface and change the implementation date.
To make the field read-only again, go back to the workbench, tick off "Editable" and click "Save".
Hope this helps. If you don't want to open the field for all requests for a short time, you could also change the value directly in the database.