Assume I liked or wrote a comment on a post of Enrique's page.
All my friends are able to see all posts which I liked or commented on News Feed.
How do I hide my activities from my friend's news feed?
You cannot do this.
Whenever you post or comment on a page or in a group that does not belong to you, you should consider that activity as potentially PUBLIC, with the possibility that -- at the very least -- your mutual friends will potentially see this in their news feed.
Moreover, the owner of that page is the only one that can determine the privacy settings for that page and/or for specific posts on that page. And so, if your friend set the privacy setting for the post that you commented on to "friends of friends," then not only will your friends potentially see this in their news feed, but their friends as well.