Reaction
Zn + Mg(NO₃)₂ ≠ no reaction
we can see the reactivity of the elements from the voltaic series
Li-K-Ba-Ca-Na-Mg-Al-Mn- (H2O) -Zn-Cr-Fe²⁺-Cd-Co-Ni-Sn-Pb- (H) -Cu-Hg-Fe³⁺-Ag-Pt-Au
The more to the left, the metal is more reactive
Mg is more reactive than Zn, so that Zn cannot displace Mg for a single displacement reaction to occur