Find the area of the region which is inside the parabola satisfying the condition `|x-2 y|+|x+2y|le 8` and `xy ge 2`.

Answer

To find the area of the region that is inside the parabola defined by the conditions \( |x - 2y| + |x + 2y| \leq 8 \) and \( xy \geq 2 \), we can follow these steps:

### Step 1: Analyze the first inequality
We start with the inequality \( |x - 2y| + |x + 2y| \leq 8 \). This can be broken down into different cases based on the signs of the expressions inside the absolute values.

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