Solve for $x$ \[ 8^{x+4}=16 \] \[ x=\pi \]

Step 1 ：Given the equation \(8^{x+4}=16\), we can rewrite it as \((2^3)^{x+4} = 2^4\).

Step 2 ：This simplifies to \(2^{3x+12} = 2^4\).

Step 3 ：Since the bases are equal, the exponents must also be equal. So, we have \(3x+12 = 4\).

Step 4 ：Solving this equation for \(x\) will give us the solution to the original equation.

Step 5 ：The solution to the equation \(3x+12 = 4\) is \(x = -\frac{8}{3}\).

Step 6 ：This is the solution to the original equation \(8^{x+4}=16\).

Step 7 ：Final Answer: The solution to the equation \(8^{x+4}=16\) is \(x = -\frac{8}{3}\). So, the final answer is \(\boxed{-\frac{8}{3}}\).