Could you please explain me which option should I use?
I would like to have a green house with rare plants from all over the world. I could take care of them (myself / by myself)?
And why?
They're both correct, but they mean slightly different things.
In "I could take care of them myself", the myself emphasizes that I'd be the one taking care of them, as opposed to someone else. It doesn't really change the meaning of the sentence, it just emphasizes a certain aspect of it.
In "I could take care of them by myself", the by myself means "without help from others".
@XPMai, yes.
I would be very surprised to see "by myself" in the sentence you gave us, @Ann. "By myself" would sound strange here. It would suggest that there is someone in the background that would like to interfere with your rare plant project. "Myself" works well, because it implies that you are capable of caring for the plants, or learning how to care for them.