@HarshG18 can you confirm you followed the steps in Installing the Pega Platform Personal Edition?

I did a search of the error '"The Process Finished Unsuccessfully.' in the forum search form  Related Content and found:

Unable to install Pega Platform Personal Edition

Database connection error while trying to install Pega 8.6 Personal Edition

 The issue of Installing Pega Plattform Personal Edition

Pega 8.7 personal edition installation error-unable to connect to db

Error While installing pega 8.7 personal edition

I'm sure one of the above posts contains a step which will resolve your issue.

There can be many reasons like - 

1. The Hostname or Port that you have specified is incorrect.

2. The connectivity from unknown clients to the database has been blocked either at Firewall or Database server.

Or in other words the IP address of the client (system where you are running the Pega installer) may not be whitelisted on the database server. 

Make sure of the following:

 -  Log in as administrator

 - Try re-downloading Personal Edition again

 - Check that there are no spaces in the directory names in the path to the install files

 - Try to change my installation path and give different port number

- Contact your database server admin to confirm / rectify if any of the above two problems are occurring. 

There are some good troubleshooting steps in the above posts, please check.

As per the error, it seems that you are not able to connect to the database. Please check if you are able to connect to DB with the details like JDBC URL, user name and password.

Check your full install logs to get the exact error.  They may be related to the below:

https://stackoverflow.com/questions/20825734/postgresql-connection-refused-check-that-the-hostname-and-port-are-correct-an

https://stackoverflow.com/questions/31268668/connection-to-hostname5432-refused

I suspect postgresSQL is already installed in your laptop - your full install logs will show message like ' unable to install postgresSQL   as already server is running in the background'

Suggest:

 1) Make sure you completely uninstalled your previous postgressql installation and try restarting your system.

 2) Update jdk with latest version and make sure system variables are correctly pointed to your jdk version 

 3) if you still face the same issue try changing the database port number to 5433 or some available port.

To validate a successful connection  issue the following telnet command.

[tet@ip-1 ~]$ telnet <HOSTNAME> port

Also see Error Installing Pega Personal Edition 8.3  which is the identical pop-up error you are seeing.