If X, Y and Z are reacting in 1 : 1 : 1 stoichiometric ratio. The concentration of X, Y and Z are found to vary as follows:

If the above equilibrium is established in 6L container by taking reactants in sufficient quantity. What is the minimum number of moles of reactants that must be taken initially to establish the equilibrium?

As there is no change in concentration of  Y with respect to time, it must be a solid or pure liquid which doesn’t appear in the expression of equilibrium constant. As concentration of X decreases it must be a reactant and Y must be the product. As the question talks about reactants, Y must be the 2^nd reactant. 
$Y\left(sorl\right)+X\underset{ }{\rightleftharpoons }Z$ 
To produce 1 mol of Z, 1 mol of Y is needed. The total number of moles of Z is 18 and hence a minimum of 18 moles of Y is needed. The number of moles of X at equilibrium is 24. There would have been 42 moles of X at the beginning.