Hi Akhil,
Thanks for the post, may I know do you mean you want to create a trust between the 2003 domain and the 2012 domain, make the users from 2003 can log in to 2012 domain and access the related resource,and users from 2012 R2 domain can log in to 2003 domain?
If that's the case, you can refer to the below article for the detailed steps to create a 2 way trust between 2 domains:
https://araihan.wordpress.com/2009/08/05/how-to-create-an-external-trust-between-two-domains/
Hope it helps.
Best Regards,
Elaine
Please remember to mark the replies as answers if they help and unmark them if they provide no help. If you have feedback for TechNet Subscriber Support, contact tnmff@microsoft.com.