Find the domain of the expression. \[ \begin{array}{l}\frac{\sqrt{x-4}}{x+6} \\ x \neq 4 \\ x \neq-6 \\ \text { all real numbers } \\ x \geq 4\end{array} \]

To determine the domain of the expression \(\frac{\sqrt{x-4}}{x+6}\), we need to ensure that the expression is defined. First, the square root function \(\sqrt{x-4}\) requires that the argument \(x-4\) is non-negative, which means \(x \geq 4\). Second, the denominator \(x+6\) should not be zero, which gives the condition \(x \neq -6\). However, since the condition \(x \geq 4\) already excludes \(x = -6\), there's no additional restriction from this second condition. Considering these factors, the only relevant constraint is \(x \geq 4\). Therefore, the domain of the expression is: \[ \text{Domain: } [4, \infty) \]