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Firstly, ensure that the emails haven't been accidentally archived or moved to a different folder within your Gmail account. Sometimes, emails can be inadvertently moved or archived, leading to confusion about their whereabouts. Check the archive and other folders in your Gmail account to see if the missing emails are located there.

If the emails are still inaccessible in your Gmail inbox but are visible in the archive and "All Inboxes" list, there may be a syncing issue between your iMac's Mail app and your Gmail account. To resolve this, try refreshing your email account in the Mail app by selecting the "Mailbox" menu and choosing "Get All New Mail." This action should prompt the Mail app to sync with your Gmail account and retrieve any missing emails.

If refreshing the email account doesn't restore the missing emails, you can try removing and re-adding your Gmail account to the Mail app. To do this, open System Preferences, select "Internet Accounts," and then remove your Gmail account from the list. Afterward, add the Gmail account again and allow it to re-sync with the Mail app.

Additionally, ensure that your Gmail account settings are configured correctly, particularly regarding the synchronization of emails between your Gmail account and the Mail app on your iMac. You can review and adjust these settings by accessing your Gmail account settings via a web browser and checking for any filters or forwarding rules that may be affecting email delivery.

If the issue persists after trying these steps, it may be helpful to contact Gmail Support or Official Apple Support for further assistance. They can provide additional troubleshooting steps or guidance specific to your email setup and software configuration.

Remember to regularly back up important emails to prevent data loss and ensure that your email account settings are configured securely to avoid unexpected issues with email synchronization and access.