4 year old touching her private parts

I never knew this was a thing until recently. I have zero experience how to handle this situation and I am super embarrassed even writing this. Some online advices say to tell her that it’s ok to do it but in private. So I did that but she does it all the time🤦🏼‍♀️I explained what private means so she gets that but I guess she can’t help it? She does it mostly while watching tv so I always tell her to stop (I am always around or go to grab something and I come back and she is doing it). I told her she can never ever do it at the day care (they have 2 hour required nap time) so I am worried she does it there too. She said she doesn’t but I know how she is and can’t really trust that. My question is, what else should I be doing to help her to understand that it’s not ok to do it in a front of other people? I can’t even imagine how embarrassing this might be for her if she won’t stop. Is there any chance this is just a phase and she will forget about it or is she going to do this from now on forever? I was ready for this during her teenage years, not now. Please help