my sql client not able to connect aws rds

Start with this...

sudo nmap -sV -Pn -p 3306 your-long-aws-hostname

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If you can't run this test, post your hostname as text (not an image) for testing.

Tip: The host you're using databaserds.c8explovbe7z.us-east-1.rds.amazonaws.com fails to resolve, so this will never work unless you have  an /etc/hosts file for resolution or you have a VPN setup or some other LAN access to this hostname.

Most likely problem - your hostname is misspelled.

Please do few pre-checks to validate
1. Hope you enabled public access while creating RDS. If not change it to "public accessible" if MySQL client running from you laptop or on-premise server.
2. If your mysql client running from EC2, check the Security Group to have rule to allow MySQL Port (3306)

Once validated above, please ensure you have updated the RDS Security Group of the server/laptop public IP (If accessing from Internet)

Now you should able to connect now.