Here are some easy ways in which you can make a Joomla template writable:
- If you are getting an error message that a particular file is not writable, change the ownership mode for this file only.
- Change the ownership and rights for the whole directory where the template is located.
In either case, the easiest way in which you can change the ownership of a file/template to make it writable is via File Manager (if your web host is using CPanel) or a similar application (if your web host is using something else). Open File Manager and navigate to the directory where the templates are. Generally it is the /templates directory under the root for your site. Select the template you want to modify, as shown in the next screenshot and click the Change Permissions button:

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This will open a dialog similar to the one below:

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Here you can change the permissions. The permissions shown in this screenshot are very liberal – i.e. they give write rights to everybody, which could be regarded as a security risk (though actually it isn't that much of a security risk if no unauthorized people can access your account).
If you want to play it safer, you can remove the ticks from the Write privilege for the Group and World entries and leave it only for User (if you are that User). If this doesn't work, make the file writable for everybody (i.e. for Group and World as well), make the template modifications you wanted and then revert the file back to unwritable.