The question asks us to determine the time shown on a clock between 3 pm and 4 pm when the distance between the hour hand and minute hand is 18 minutes.

Let's break down the problem step by step:

1. Calculating the Angle Between the Hour and Minute Hand:
- In a clock, the minute hand completes a full rotation in 60 minutes, which corresponds to 360 degrees.
- Therefore, each minute corresponds to an angle of 360 degrees / 60 minutes = 6 degrees.
- Similarly, the hour hand completes a full rotation in 12 hours, which corresponds to 360 degrees.
- Hence, each hour corresponds to an angle of 360 degrees / 12 hours = 30 degrees.
- The minute hand moves at a constant rate of 6 degrees per minute.
- The hour hand moves at a rate of 0.5 degrees per minute (30 degrees / 60 minutes).

2. Calculating the Time Difference:
- Since the distance between the hour and minute hand is 18 minutes, we can find the time difference as follows:
- Let x be the time on the clock in minutes.
- The minute hand would have moved x minutes, covering an angle of 6x degrees.
- The hour hand would have moved (x/60) minutes, covering an angle of (0.5 * x/60) degrees.
- The absolute difference between these two angles is 18 degrees.

3. Solving the Equation:
- To find the time on the clock, we need to solve the equation: |6x - (0.5 * x/60)| = 18.
- We can simplify this equation to: |360x - x/60| = 18.
- Combining like terms, we have: |359x/60| = 18.
- Dividing both sides by 359/60, we get: |x| = (18 * 60) / (359).
- Evaluating the expression, we find: |x| ≈ 3.01.

4. Determining the Time:
- Since the time is between 3 pm and 4 pm, the minute hand should be ahead of the hour hand.
- Therefore, the time on the clock would be slightly past 3 o'clock.
- The closest option is 3:36 pm (option D), which aligns with our calculation.

Therefore, the correct answer is option D: 3 : 36 pm.