1. The problem asks to find the limit as $n$ approaches infinity of the expression $\frac{n + 8}{n + 4}$.\n\n2. To analyze the limit, divide both numerator and denominator by $n$: $$\lim_{n \to \infty} \frac{n + 8}{n + 4} = \lim_{n \to \infty} \frac{\frac{n}{n} + \frac{8}{n}}{\frac{n}{n} + \frac{4}{n}} = \lim_{n \to \infty} \frac{1 + \frac{8}{n}}{1 + \frac{4}{n}}.$$\n\n3. As $n$ becomes very large, $\frac{8}{n}$ and $\frac{4}{n}$ approach zero, so the expression simplifies to: $$\frac{1 + 0}{1 + 0} = 1.$$\n\n4. Therefore, the limit is $\boxed{1}$.