Well, first of all, keep the main characters and their key traits. For example, if it's a story about a brave knight, don't change him into a coward. Then, focus on the main plot points. You can rephrase the events, but don't skip the crucial ones. Also, add some new details that can enhance the story, like a new setting or a small side - story related to the main plot.
To make it engaging and true to the original essence, you should understand the message of the original story. Is it about love, friendship, or courage? Once you know that, you can rewrite it while still highlighting that message. Try to use different words to describe the same actions and feelings. For instance, instead of saying 'the hero was happy', you could say 'the hero's face lit up with joy'. And don't forget to read the original story multiple times to really soak in all the details.
One important thing is to maintain the pacing of the original story. If it was a fast - paced adventure, don't slow it down too much in your rewrite. You can change the sequence of some events to add freshness, but not in a way that confuses the reader. Another tip is to give more depth to the characters. If there was a mysterious character in the original, you could add some backstory to make them even more interesting in your rewritten version.