@patriciac1 I recommend you review the settings for global tasks first. Within Setup > Project Preferences > Tasks & Issues, there is a section for Access. Check to see what level of access a user is granted when submitting a request or is assigned to a task or issue. If you have it set to View, you may want to think about changing that to Contribute, especially if that is going to be the case for all projects within your system.
If it is just this specific project giving you access issues, check to see if there is a project template attached. If there is a template attached, review the access settings of the template to ensure that Contribute is selected vs View for users who are assigned to a task.
If there is not a project template associated with this project, edit the project and navigate to the access section and update the permissions there.
Hope that helps!
