A common ion effect can reduce the amount of a specific ion in solution through precipitation with another counterion. This question includes multiple ions, so common ion effect was a thought I had as well, but the question doesn't specifically mention a reduced solubility because of an ion being added. The part about extra anions and cations is fluff to knock you off the scent. The core of this question is asking why a precipitate forms in general, and that happens when you have more of the component ions in solution than can possibly dissolve (the molar solubility.)