In the following idiom and phrase question, select the option that best explains the meaning of the expression "rule of thumb".

Introduction / Context:
The expression "rule of thumb" is a very common English idiom used in science, business, and everyday life. It refers to a general principle or guideline that is not exact but works reasonably well in many practical situations. Examinations test this idiom because it appears often in articles and speeches where writers talk about approximate methods or quick estimates. Understanding its meaning helps learners interpret texts that describe practical decision making.

Given Data / Assumptions:
- The idiom in focus is "rule of thumb". - Four possible explanations are provided. - The correct answer must capture the idea of a general, practical guideline, not a strict law. - Only one option clearly presents this meaning.

Concept / Approach:
A "rule of thumb" is not a mathematical rule or a legal rule; it is an approximate method that people use based on experience. For example, a cook may use a rule of thumb to estimate salt without measuring precisely, or a manager may use a rule of thumb for budgeting. Therefore, the correct option should describe an approximate guide drawn from practice. Options that emphasise physical punishment, strict discipline, or literal measurement of length do not match the widely accepted modern usage of the idiom.

Step-by-Step Solution:
Step 1: Read the idiom "rule of thumb" and recall typical sentences such as "As a rule of thumb, you should save at least ten percent of your income." Step 2: Examine option a, "A rough unit of measure for small lengths". This suggests a literal measuring unit, which is not the core meaning in modern English usage. Step 3: Examine option b, "A broadly accurate guide based on practice". This describes a general guideline, not exact, but useful, constructed from experience. It fits very well. Step 4: Examine option c, "To force someone to work against his wish". This relates to coercion and has no link to guidelines or estimation. Step 5: Examine option d, "To use your power to ensure discipline". This also deals with authority and control, which is unrelated to the meaning of a practical guideline. Step 6: Conclude that option b is the only one that captures the idea behind the idiom "rule of thumb".

Verification / Alternative check:
To verify, place each explanation into a realistic sentence. For example, "A good rule of thumb in negotiation is to listen twice as much as you speak." Replacing "rule of thumb" with "a broadly accurate guide based on practice" still makes sense; negotiation coaches develop such guides from experience. However, inserting ideas about forcing someone to work or using power to ensure discipline would not make sense in that context. Similarly, a "rough unit of measure for small lengths" is too literal and narrow for the many contexts in which the idiom is used. This confirms that option b is appropriate.

Why Other Options Are Wrong:
Option a is wrong because it treats the phrase as a literal measuring unit instead of recognising it as an approximate principle. Option c is wrong because it introduces compulsion and unwilling work, which are unrelated to the concept of a guideline based on experience. Option d is wrong because it focuses on the use of power or authority, again not part of the idiom meaning.

Common Pitfalls:
Some learners may have heard historical explanations linking the phrase to measurements using the thumb, and they may wrongly choose an option that focuses on length. However, modern exam questions test the contemporary figurative meaning, not the origin story. Candidates must learn to separate etymology from usage and to choose the option that best fits how the idiom is used today in written and spoken English.

Final Answer:
The idiom "rule of thumb" means a broadly accurate guide based on practice.