SAT Question b988eeec: Linear Functions answer and explanation with Desmos solution

It's given that the functions $f$ and $g$ are defined as $f\left(x\right)=\frac{1}{4}x-9$ and $g\left(x\right)=\frac{3}{4}x+21$. If the function $h$ is defined as $h\left(x\right)=f\left(x\right)+g\left(x\right)$, then substituting $\frac{1}{4}x-9$ for $f\left(x\right)$ and $\frac{3}{4}x+21$ for $g\left(x\right)$ in this function yields $h\left(x\right)=\frac{1}{4}x-9+\frac{3}{4}x+21$. This can be rewritten as $h\left(x\right)=\frac{4}{4}x+12$, or $h\left(x\right)=x+12$. The x-intercept of a graph in the xy-plane is the point on the graph where $y=0$. The equation representing the graph of $y=h\left(x\right)$ is $y=x+12$. Substituting $0$ for $y$ in this equation yields $0=x+12$. Subtracting $12$ from both sides of this equation yields $-12=x$, or $x=-12$. Therefore, the x-coordinate of the x-intercept of the graph of $y=h\left(x\right)$ in the xy-plane is $-12$.