There are many practical applications of functional equations that depend on the Ulam stability. Important for real-world applications, this stability idea makes sure that slight modifications to the functional equation don't cause significant modifications to the solutions. The purpose of this work is to examine the Hyers-Ulam stability of a finite-dimensional quartic functional equation in 2-Banach spaces and IFN-spaces (Intuitionistic Fuzzy Normed spaces) by utilizing fixed point and direct approaches. Within the context of this quartic functional equation, as an illustration of the stability of the equation can be regulated by sums and products of powers of norms, we present several instances.