In facebook, different stories can be added by any page, group or friend. But some options are specifically enabled for pages and groups stories. In case you see a story made by your favorite page and want to give a big thumbs up then follow these steps:
Go to the stories section of facebook as shown in below image.
Click on the story you want to give like. It will be opened in your mobile phone.
Finally, at the right bottom of the story you can see "Thumbs Up" button in blue color. Tap on it and your reaction will be posted to the respective page.