1. **State the problem:** Simplify the expression $\sqrt{16} + 12\sqrt{55}$.\n\n2. **Recall the square root rule:** $\sqrt{a}$ is the number which when squared gives $a$. For perfect squares like 16, $\sqrt{16} = 4$.\n\n3. **Simplify the first term:** $\sqrt{16} = 4$.\n\n4. **Analyze the second term:** $12\sqrt{55}$ cannot be simplified further because 55 is not a perfect square and has no perfect square factors other than 1.\n\n5. **Combine the terms:** The expression becomes $4 + 12\sqrt{55}$.\n\n6. **Final answer:** $4 + 12\sqrt{55}$ is the simplified form since the terms are unlike and cannot be combined further.