The correct answer is option 2: more than 6 feet but less than 7 feet.

To understand why, let`s visualize the situation. We have two vertically placed pillars that are 8 feet apart. The height difference between the two pillars is 6 feet.

The rope is tied to the tips of the two pillars and has a length of 15 feet. We need to determine the portion of the taller pillar`s height that can be brought in contact with the rope without detaching it from the pillars.

Since the taller pillar is 6 feet higher than the shorter one, we know that the rope covers this height difference. However, the rope is not fully stretched between the pillars, as it is tied to their tips.

To find the maximum height of the taller pillar that can be brought in contact with the rope, we need to consider the hypotenuse formed by the rope and the height difference between the pillars.

Using the Pythagorean theorem, we can find that the length of this hypotenuse is approximately 10 feet.

Therefore, the portion of the taller pillar`s height that can be brought in contact with the rope is more than 6 feet but less than 7 feet.