Könnte bitte jemand den Unterschied zwischen schätzen, anerkennen und würdigen erklären?
The best answer you can get is probably from a dictionary, because those words may have slightly to completely different meanings, depending on the context. I'll give it a shot, though.
Schätzen: Can either mean to evaluate something (e.g. a distance), to assume something, or to appreciate someone (usually in a positive context).
Anerkennen: Can be used to also express appreciation for something. It does not always have to be used in such a positive context, though. Also, it sounds more formal. Also, it can mean to simply acknowledge something (e.g. an independent nation by other nations)
Würdigen: Is used to express appreciation for something/someone, too. It has a very positive connotation in most of the cases and also sounds more formal than "schätzen" does.
However, if you could give a bit more context on what you are specifically looking for, you'd probably receive more fitting answers.