  Addressing stability in functional equations is a critical task with broad
implications across mathematics and its applications. In this paper, we present
a novel direct method for proving the stability of the following equation,
\begin{eqnarray*} f(x,y)=\alpha f(f_1(x,y))+\beta f(f_2(x,y)) \end{eqnarray*}
subjecting to certain constraints on the constants $\alpha$ and $\beta$, as
well as the functions $f_1(x,y)$ and $f_2(x,y)$. We introduce the direct method
to prove the stability of the following functional equation and inequality,
\begin{eqnarray*} \|f(x+y,z-w)+f(x-y,z+w)-2f(x,z)+2f(y,w)\| \leq
\|x\|^p\|y\|^p\|z\|^p\|w\|^p; \end{eqnarray*} \begin{eqnarray*} \begin{split}
\;&\|f\left(x+y,z-w\right)+af\left(\frac{x-y}{a},z+w\right)-2f(x,z)+2f(y,w)
\|\\ \;&\leq \left\|
\rho\left(f(x+y,z-w)+f(x-y,z+w)-2f(x,z)+2f(y,w)\right)\right\|. \end{split}
\end{eqnarray*} This technique efficiently confirms stability, outperforming
traditional proof methods in simplicity and efficacy. The application of our
direct approach to various equations solidifies its validity, ensuring stable
behavior across different mathematical contexts.
