1. The problem is to analyze the function $$g(x) = |x| + |\sin(4\pi)|.$$\n\n2. First, recall that the absolute value function $|x|$ returns the non-negative value of $x$.\n\n3. Next, evaluate $\sin(4\pi)$. Since $\sin(\theta)$ has period $2\pi$, $\sin(4\pi) = \sin(0) = 0$.\n\n4. Therefore, $|\sin(4\pi)| = |0| = 0$.\n\n5. Substitute back into the function: $$g(x) = |x| + 0 = |x|.$$\n\n6. So the function simplifies to $$g(x) = |x|,$$ which is the absolute value function.