To solve this problem, let's consider the given information and break it down step by step:

Given information:
- The length of the smaller side of the rectangle is 16 cm.
- A line parallel to the smaller side divides the rectangle into two rectangles, P and Q.
- One of the rectangles is similar to the original rectangle.
- The sides of both rectangles P and Q are integral values.

Step 1: Understanding the problem
To find the number of distinct pairs of rectangles P and Q, we need to determine the possible combinations of integral values for the sides of both rectangles.

Step 2: Identifying the similar rectangle
Since one of the rectangles is similar to the original rectangle, we can assume that rectangle P is similar to the original rectangle. This means that the ratio of the sides of rectangle P to the original rectangle is the same.

Step 3: Finding the possible combinations
To find the possible combinations, we need to consider the ratio of the sides of rectangle P and the original rectangle. Let's assume the length and width of the original rectangle are L and W, respectively.

The ratio of the sides of rectangle P to the original rectangle is given by:
Length of P / L = Width of P / W

Since the length of the smaller side of the original rectangle is 16 cm, we can assume that L = 16 cm.

Therefore, the ratio becomes:
Length of P / 16 = Width of P / W

To find the possible combinations of integral values for the sides of both rectangles, we need to find the integral values of Length of P and Width of P that satisfy the above equation.

Step 4: Determining the possible values
Since the sides of both rectangles P and Q are integral values, we can start by assuming some integral values for the length and width of rectangle P and check if the equation is satisfied.

Let's consider some possible values for the length of P: 32, 48, 64, 80, 96, ...

For each assumed value of the length of P, we can calculate the corresponding value of the width of P using the equation:
Width of P = (Length of P * W) / 16

If the width of P is an integral value, then it is a valid combination. We need to find the number of such valid combinations.

Step 5: Finding the number of valid combinations
By trying out different values for the length of P, we can find that there are four valid combinations for the sides of rectangles P and Q:

1) Length of P = 32, Width of P = 40
Length of Q = 16, Width of Q = 20

2) Length of P = 48, Width of P = 60
Length of Q = 16, Width of Q = 20

3) Length of P = 64, Width of P = 80
Length of Q = 16, Width of Q = 20

4) Length of P = 96, Width of P = 120
Length of Q = 16, Width of Q = 20

Therefore, there are four distinct pairs of rectangles P and Q that satisfy the given conditions.

Hence, the correct answer is option C) 4.