Identify the equation for which #K_c = ["Ni"^(3+)]["Cl"^-]^3#.?

A reaction with forumla
#a"A"+b"B"\rightleftharpoons c"C"+d"D"#

will have an equilibrium constant of
#"K"_c=(["C"]^c * ["D"]^d)/(["A"]^a * ["B"]^b)#

Both #["Ni"^(3+)]# and #["Cl"^-]# are found in the numerator of the equilibrium constant. Therefore you might expect to find them on the product side of the reaction to the right of the reversible sign.

The number of moles of individual species shall equal to the respective powers of its concentration in the equilibrium constant expression. Thus in this question, there's one mole of #"Ni"^(3+)#
and three moles of #"Cl"^-# on the right-hand side of the equation.

The concentration of pure solids and liquids does not affect the equilibrium position.[1] Therefore these species are assigned activity values of #1#. The equilibrium constant here has a denominator of #1#, which corresponds to the pure solid #"NiCl"_3(s)# that is supposed to lie on the reactant side of the reaction.

References
[1] Clark, Jim. “Writing Equilibrium Constant Expressions Involving Solids and Liquids.” Chemistry LibreTexts, Libretexts, 21 July 2016, chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Equilibria/Chemical_Equilibria/Calculating_An_Equilibrium_Concentrations/Writing_Equilibrium_Constant_Expressions_involving_solids_and_liquids .