Displaying profile photo on others' phone when called I am using Android 6.0.1. How and where to set my profile image, so that the image is seen by the opposite person when he is called on the phone?
You can not do that. It is not possible to set a profile photo for yourself on other phones. Phone calls transmit nothing but your voice and phone number. You can not transmit a profile picture through a phone call. Third-party apps like Google Hangouts do not use phone lines, instead, they use data, so they use a custom protocol that allows them to send the profile pic of the caller.
The receiver of the call must set a profile photo for you. This must be done for everyone that you want to see the profile photo of:

For iPhone users: http://osxdaily.com/2015/11/07/assign-photo-to-iphone-contact/
For Android users: http://www.howtogeek.com/259513/how-to-change-contact-pictures-in-android/.

They will want to follow the instructions to add a photo to your contact, not theirs.