1. **State the problem:** Find the values of $x$ that are not allowed in the expression $\frac{x+4}{x^2-16}$. 2. **Understand the rule:** The denominator of a fraction cannot be zero because division by zero is undefined. 3. **Set the denominator equal to zero:** $$x^2 - 16 = 0$$ 4. **Solve for $x$:** $$x^2 = 16$$ $$x = \pm 4$$ 5. **Interpret the result:** The values $x=4$ and $x=-4$ make the denominator zero, so these values are not allowed. **Final answer:** The values of $x$ that are not allowed are $x=4$ and $x=-4$.