Moodle Assignment: granting extensions for an assignment
Select the assignment that you wish to add an extension for.
Select View all submissions.
If you wish to grant an extension to just one student, tick the checkbox next to the student name. In the Edit drop-down menu, select Grant extension.
For multiple students, tick the checkbox for each student on the left and then select Grant extension in the With selected... drop-down menu at the bottom of the page. Then, select Go, and OK in the little pop-up window that will appear at the top of your page.
On the next screen you can set the new due date via Extension due date. To save this new due date, select Save changes.