Solve: Finding -|4²| Using Order of Operations

To solve this problem, we'll follow these steps:

• Step 1: Compute the expression inside the absolute value.
• Step 2: Apply the absolute value.
• Step 3: Apply the negative sign.

Now, let's work through each step:
Step 1: Compute $4^2$.
Since $4^2 = 16$, we have $\lvert 4^2 \rvert = \lvert 16 \rvert$.
Step 2: Apply the absolute value operation. The absolute value of 16 is 16, so $\lvert 16 \rvert = 16$.
Step 3: Apply the negative sign. We then have $-\lvert 16 \rvert = -16$.

Therefore, the solution to the problem is $-16$.