In this English grammar sentence improvement question, consider the sentence We insist on you leaving the meeting immediately, where the underlined part you leaving may not follow the most natural and grammatically correct pattern after the preposition on. Choose the option that best improves the underlined expression while preserving the original sense of strong insistence, and select No improvement only if the sentence is already fully acceptable in standard formal English.

Introduction / Context:
This question checks the correct grammatical pattern after the verb insist when it is followed by a preposition and a verbal noun. In careful written English, some verbs and prepositions are followed by a gerund with a possessive form rather than a simple object pronoun. The sentence expresses strong insistence that someone leave a meeting at once, and the task is to choose the structure that best matches standard educated usage in this context.

Given Data / Assumptions:

• The base sentence is We insist on you leaving the meeting immediately.
• The underlined portion is you leaving.
• The options offer structures with you to leave, your leaving, you leave, and No improvement.
• The register of the test is formal standard English, not casual conversation.

Concept / Approach:
After prepositions such as on, of, for, and in, English normally uses a gerund form, which is the ing form of a verb acting as a noun. When a person is linked to that gerund, many style guides and grammar books recommend a possessive form, as in your leaving, his coming, or their arriving. The construction insist on can also take that pattern. Therefore, we look for an option that respects both the use of the preposition on with a gerund and, in formal English, a possessive determiner before the gerund. The correct answer should sound natural in a formal context and should not break basic rules of verb complementation.

Step-by-Step Solution:
First, identify that insist on is followed by a verbal phrase that functions like a noun, describing the action of leaving. Second, recall that after a preposition we typically use a gerund, so the core form should be leaving and not leave or to leave. Third, recognise that in formal English a possessive determiner is usually placed before a gerund to show ownership of the action, so we prefer your leaving over you leaving. Fourth, compare the options and note that only your leaving combines the possessive determiner with the gerund in a way that fits insist on. Finally, confirm that the revised sentence We insist on your leaving the meeting immediately sounds grammatically standard and clear.

Verification / Alternative check:
To verify, you can compare similar structures: We object to his smoking here or They approved of our going early. In each case, a preposition is followed by a possessive determiner plus a gerund. Grammar references often give examples such as I insist on your staying for dinner in formal contexts. Modern spoken English sometimes allows you leaving, but formal examination standards still tend to prefer the possessive form. Because this is an exam question that usually follows traditional grammar norms, your leaving matches the expected pattern better than the casual alternative.

Why Other Options Are Wrong:
Option A, you to leave, tries to use an infinitive after a preposition, which is ungrammatical in English because prepositions are normally followed by gerunds or noun phrases, not to plus base verb.
Option C, you leave, uses a bare verb form after a preposition, which again does not follow the standard preposition plus gerund rule and therefore sounds incorrect in careful usage.
Option D, No improvement, would accept the original you leaving, which is more informal and not the most accurate answer in a formal test setting.

Common Pitfalls:
Many learners confuse patterns after verbs like insist, suggest, or recommend, because these verbs can sometimes take different structures, such as insist that he leave or insist on his leaving. Mixing the two patterns, for example insist on he leave, leads to errors. Another common problem is forgetting that prepositions must be followed by a gerund or noun phrase, not by a full infinitive. Learners also often overlook the possessive before a gerund in formal English and default to object pronouns, which exam setters use as traps.

Final Answer:
The best and most formally correct improvement uses a possessive determiner before the gerund after the preposition on, so the correct choice is your leaving.