sich vorstellen / sich etwas vorstellen

The verb sich vorstellen has two common meanings, and the reflexive pronoun tells you which one it is. With the accusative, someone introduces themselves or someone else: Darf ich mich vorstellen? means May I introduce myself? You can also introduce another person: Ich möchte dich meinen Eltern vorstellen. Here the person being introduced is the accusative object and the audience is in the dative.

With the dative and a second object, the verb means to imagine: Ich kann mir das nicht vorstellen. Here mir is dative and das is the thing imagined. A frequent learner mistake is using the accusative in this meaning and saying Ich kann mich das nicht vorstellen, which is ungrammatical. Remember: introducing uses mich, imagining uses mir.