Hey Naveen,
Did you set a password and noted your username for that org before changing the domain name for that org? 

If yes, then follow these steps:
1. Click on the last option "Manage my hands-on orgs" from the drop down list (list from which we choose our playground org).
2. Click on "Connect an org" button(right below the list of all your connected orgs).
3.You will be redirected to login page of salesforce. Login with your credentials of that playground. Your playground will now be visible in that list of connected list of orgs. Select and launch.

If not, then follow these steps(this is a bit tricky):
Note: You must remember the new domain name of that org. If not, then I suggest you write a mail explaining your situationto salesforce about your problem.

Continuing,
1. In the URL enter : https://YOUR_NEW_DOMAIN_NAME-dev-ed.my.salesforce.com/. Hit enter. You will be redirected to a login page.
2. Click on forgot password.
3. This is where it gets a little tricky if you don't know your username for that playground. Your username will look like this:
    Left portion of your email ID from '@' and the username shown on the list of connected orgs of your playground in Trailhead (Refer to the Screenshot).
    So, if my email is amit.agr@xyz.com and  username : curious-bear-420843.com (of that particular playground).
    Then login username will be: amit.agr@curious-bear-420843.com.
4. Enter this username and click continue.
5. You will receive a password reset link on your email.

I guess you can take it from then on I guess. Please do not forget this username. Because this will be your username to login.