I have created a PostgreSQL Amazon RDS databaes but I cannot connect to it from my local machine.

I am connecting like this:

Response is:

Is the server running on host and accepting TCP/IP connections on port 5432?

Here are the database settings:

Here are my security group settings:

Your configuration picture is showing a setting of Publicly Accessible = No.

You will need to modify your database to set this to Yes.

From Modifying a DB Instance Running the PostgreSQL Database Engine:

Publicly Accessible

Choose Yes to give the DB instance a public IP address, meaning that it will be accessible outside the VPC (the DB instance also needs to be in a public subnet in the VPC); otherwise, choose No, so the DB instance will only be accessible from inside the VPC.