Given:
The inequality is given as |x| |y| = 7.

To find:
The number of pairs of integers that satisfy the inequality.

Solution:
We can start by considering all possible values of x and y.

Case 1: x > 0 and y > 0
In this case, |x| = x and |y| = y.
So, the inequality becomes xy = 7.

We need to find all pairs of positive integers whose product is 7. The pairs are (1, 7) and (7, 1).

Case 2: x > 0 and y < />
In this case, |x| = x and |y| = -y.
So, the inequality becomes x(-y) = 7, which simplifies to -xy = 7.

We need to find all pairs of positive and negative integers whose product is -7. The pairs are (-1, 7) and (7, -1).

Case 3: x < 0="" and="" y="" /> 0
In this case, |x| = -x and |y| = y.
So, the inequality becomes (-x)y = 7, which simplifies to -xy = 7.

We need to find all pairs of positive and negative integers whose product is -7. The pairs are (-7, 1) and (1, -7).

Case 4: x < 0="" and="" y="" />< />
In this case, |x| = -x and |y| = -y.
So, the inequality becomes (-x)(-y) = 7, which simplifies to xy = 7.

We need to find all pairs of negative integers whose product is 7. The pairs are (-1, -7) and (-7, -1).

Total number of pairs:
Adding up all the pairs from the four cases, we get a total of 2 + 2 + 2 + 2 = 8 pairs.

Since each pair can be positive or negative, we have 8 * 2 = 16 pairs.

Therefore, the correct answer is option D) 28.