Number of Parallelograms Formed by Intersecting Parallel Lines:

To find the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, we can follow a step-by-step approach.

Step 1: Understand the Problem
We are given two sets of parallel lines, each containing four lines. We need to determine the number of parallelograms that can be formed by selecting four lines, two from each set, such that they form a parallelogram.

Step 2: Identify the Conditions for a Parallelogram
In order for four lines to form a parallelogram, they must satisfy the following conditions:
- Opposite sides are parallel.
- Opposite sides are equal in length.
- Opposite angles are equal in measure.

Step 3: Count the Possible Options
Let's consider the two sets of parallel lines as A and B, with four lines each. We need to select two lines from set A and two lines from set B to form a parallelogram.

Case 1: Selecting Two Adjacent Lines from Each Set
In this case, we can select two adjacent lines from set A and two adjacent lines from set B. There are four ways to select two adjacent lines from set A and four ways to select two adjacent lines from set B. Therefore, the total number of options in this case is 4 * 4 = 16.

Case 2: Selecting One Line from Each Set
In this case, we can select one line from set A and one line from set B. There are four ways to select one line from set A and four ways to select one line from set B. Therefore, the total number of options in this case is 4 * 4 = 16.

Step 4: Total Number of Parallelograms
To find the total number of parallelograms, we need to add the options from both cases. Therefore, the total number of parallelograms that can be formed is 16 + 16 = 32.

Conclusion:
The correct answer is option C) 32.