“Can I give my 4 years old daughter multivitamins?”

Of course, you can, but that is not the question. The question is, is there any health benefit of giving my 4 year old daughter a multivitamin pill (daily, I suppose you mean)? The answer is no unless you are unable to provide and get your daughter to eat a healthy, varied diet. The internet is awash with good advice as to the food pyramid and much healthy dietary advice. Even if you cannot get your daughter to eat her way to a full vitamin level, there are ways to work around this without resorting to vitamin supplementation - for example, a child psychologist.