1. The problem asks to find $(fg)(4)$, which means the composition of functions $f$ and $g$ evaluated at $x=4$. 2. Recall that the composition $(fg)(x)$ means $f(g(x))$, so we first find $g(4)$ and then plug that result into $f$. 3. Given $g(x) = 3x + 1$, calculate: $$g(4) = 3(4) + 1 = 12 + 1 = 13$$ 4. Now, use $f(x) = 2x^2 - 4$ and substitute $x = g(4) = 13$: $$f(13) = 2(13)^2 - 4 = 2(169) - 4 = 338 - 4 = 334$$ 5. Therefore, the value of $(fg)(4)$ is $334$. Final answer: $334$