JEE Advanced 2024 · Paper 2, Mathematics question 8

Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that $f(x+y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$, and $g : \mathbb{R} \to (0, \infty)$ be a function such that $g(x+y) = g(x)g(y)$ for all $x, y \in \mathbb{R}$. If $f\left(\dfrac{-3}{5}\right) = 12$ and $g\left(\dfrac{-1}{3}\right) = 2$, then the value of $\left(f\left(\dfrac14\right) + g(-2) - 8\right)g(0)$ is _____.