Hi @Tanushree Raj ,
Welcome to the community!
Basically it happens because of a few things:
1. Clear browsing data/cache and re-login.
2. Check the member permissions.
3. Make sure everyone has the same plan for Trello.
4. disable any third-party extensions using in the browser.
If still having problem ask Trello support: HERE
I think your coworker just needs to JOIN the board in order to see the elements that allow them to edit the board.
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