In the following question on idioms, choose the alternative which best expresses the meaning of the phrase "At loggerheads".

Introduction / Context:
The idiomatic expression at loggerheads is widely used in newspapers, discussions and formal writing to describe serious disagreement or conflict between people, groups or countries. Recognising its meaning is important for correctly interpreting reports about disputes, negotiations and long standing rivalries.

Given Data / Assumptions:

• Idiom: At loggerheads.
• Options: To suffer, In conflict with someone, To face tough competition, To be in do or die situation, and To be confused.
• The phrase is almost always used with a plural subject, such as two parties, groups or individuals.
• The sense is that they are in strong disagreement or are hostile towards each other.

Concept / Approach:
Historically, loggerheads were tools or weapons, and being at loggerheads suggested confronting each other with opposing instruments. In modern English, at loggerheads means to be in stubborn dispute or conflict, often over an issue that neither side wants to compromise on. It does not simply mean suffering, facing competition, being in a desperate situation or feeling confused. Instead, it specifically refers to a state of hostility or serious disagreement between two parties.

Step-by-Step Solution:
Step 1: Recall the current usage of at loggerheads in sentences like The two neighbours are at loggerheads over the boundary wall.
Step 2: Identify that the phrase describes a situation of conflict or serious disagreement.
Step 3: Compare each option: To suffer, In conflict with someone, To face tough competition, To be in do or die situation, To be confused.
Step 4: See that only In conflict with someone directly captures the idea of being in serious disagreement.
Step 5: Select this option as the best explanation of the idiom.

Verification / Alternative check:
Try substituting the meaning into an example: The management and the workers are at loggerheads over the new policy becomes The management and the workers are in conflict with each other over the new policy. This substitution keeps the sense and tone of the sentence intact. If we try are suffering, are in a do or die situation or are confused, the meaning changes completely. Therefore, at loggerheads must be understood as being in conflict with someone.

Why Other Options Are Wrong:
Option A, To suffer, describes experiencing pain or hardship but does not necessarily imply conflict with another person. Option C, To face tough competition, refers to rivalry in performance rather than direct dispute, and competitors can exist without being at loggerheads. Option D, To be in do or die situation, suggests extreme urgency or life and death stakes, not necessarily disagreement. Option E, To be confused, refers to mental uncertainty, which is unrelated to interpersonal conflict. None of these capture the mutual opposition that characterises being at loggerheads.

Common Pitfalls:
Some learners may misinterpret at loggerheads as simply having a problem, suffering or being under pressure. It is helpful to remember that the phrase always involves at least two parties whose interests or opinions clash. Reading editorials and news articles where this idiom appears in context will strengthen understanding and make it easier to recognise in examinations.

Final Answer:
The idiom At loggerheads means in conflict with someone.