Final answer:
The most difficult or impossible scale to construct among the given options is a balanced, six-point, nonforced-choice scale because a balanced scale with an even number of options cannot have a nonforced-choice that includes a neutral position.
Step-by-step explanation:
The question you asked pertains to the construction of different types of scales often used in surveys or questionnaires, specifically within social sciences or data collection methods. An example of such scales is the Likert-type scale, which is frequently used to measure attitudes or opinions. When discussing the difficulty of constructing various scales, the key is to understand the terms 'balanced', 'forced-choice', and 'nonforced-choice'.
A 'balanced' scale typically has an equal number of positive and negative options, while an 'unbalanced' scale has a greater number of options on one side of the spectrum. A 'forced-choice' scale requires respondents to choose an option, effectively disallowing a neutral or abstained response. A 'nonforced-choice' scale, on the other hand, includes a neutral option or the possibility to abstain.
Considering these definitions, the most difficult or impossible to construct would be option B, A balanced, six-point, nonforced-choice scale. This is because a balanced scale with an even number of options inherently omits a neutral middle ground, making it contradictory to have a nonforced-choice option.