Answer
The addition of copper(II) nitrate would move the equilibrium to the right, favoring the $[Cu(NH_3)_4]^{2+}$ production.
Work Step by Step
This is the equilibrium reaction:
$Cu^{2+}(aq) + 4NH_3(aq) \lt -- \gt [Cu(NH_3)_4]^{2+}(aq)$
When we add $Cu(NO_3)_2$, it has $Cu^{2+}$, so, the common ion effect will act, and the reaction will be more product-favored.
That follows the Le Chatelier's principle. Since we are raising the concentration of one of the reactants, the equilibrium will try to reduce this concentration, to reduce the change.
Therefore, the equilibrium will move to the right.
