English: What are you doing this weekend?
Czenglish: I’m taking care about my little sister.
English: You are taking care of your little sister.
Czenglish: Oh, so what does ‘take care about’ mean?
Take care about should never be said. It is a bad combination of ‘take care of’ and ‘care about’.
To care about is to be interested in or to have strong feelings about something. For example, I care about education (I am interested in education).
To take care of is to look after. For example, I take care of my Mum (I look after my Mum).