In this question, we have a situation where a person accidentally mixes two chemical substances, Na2CO3 and MgSO4. In water, this reaction will indeed occur, and the products will be following:
Na2CO3 (aq) + MgSO4 (aq) -> Na2SO4 (aq) + MgCO3 (s), we see here that it is a Double replacement reaction.
One of the observations from the person is that, tiny white solids formed at the bottom of the washing machine, this is due to the precipitation of MgCO3, even though some carbonates are soluble in water, MgCO3 is not, therefore it will form a precipitate, which are white solids, at the bottom of the solution