Consider the following expressions:

To evaluate the expression:

\[
-6 + 3 \times 5 \quad \_\_\_\_ \quad \sqrt{16} + \frac{32}{8}
\]

let's first compute each side:

1. **Left Side Calculation:**
\[
-6 + 3 \times 5
\]
According to the order of operations, we perform the multiplication first:
\[
3 \times 5 = 15
\]
Then, we add:
\[
-6 + 15 = 9
\]

2. **Right Side Calculation:**
\[
\sqrt{16} + \frac{32}{8}
\]
First, calculate the square root:
\[
\sqrt{16} = 4
\]
Next, divide:
\[
\frac{32}{8} = 4
\]
Now, add:
\[
4 + 4 = 8
\]

Now we have:
\[
9 \quad \_\_\_\_ \quad 8
\]
- We know that \( 9 > 8 \), so we can insert the "greater than" operator.

Thus, we conclude that the appropriate operator to insert is:
\[
>
\]