If you want to view the photos that someone is liking on Instagram, you have to follow the person. So make sure that you are following the person. Click on the "News" tab located at the bottom of your screen. You will see two tabs i.e "Following" and "You". Click on the "Following" tab. You will see activities from all your followers and the photos they have liked. But here you can not view all the photos liked by other users. You can not view old likes of photos.