Apple Mail Keeps Saying GMail Password Wrong

For both Gmail & Microsoft Live mail, you may need to generate an app-specific password to use in the Apple Mail app instead of your normal passwords that you use for these accounts.

Ref: Using app-specific passwords - Apple Support

Were you able to access both of these email accounts successfully using their web browser interface? If so, then you will need to go to both providers' support sites to generate this app-specific password to use in the Mail app.

• For Microsoft, go to: https://account.live.com/proofs/apppassword
• For Gmail, go to:  https://security.google.com/settings/security/apppasswords

Then the issue is with your Gmail account settings. Most likely, it has to do with additional security imposed by Google, like two-factor authentication. You will need to get this resolved before you can use any email clients to gain access to your email account.