Topic: Preposition,

Best Answer Explained in Below-:

The phrase "I count upon your help" conveys a sense of reliance and trust in someone's assistance. The verb "count" is often paired with the preposition "upon" to express the idea of depending on someone for support or aid. This usage suggests a strong expectation that the help will be available when needed.

Examining the other options:
- **A) after** does not fit because it implies a sequence in time rather than reliance. You would not typically say "I count after your help."
- **C) for** can imply a request or need but does not carry the same weight of dependency. For example, "I ask for your help" is more about seeking assistance rather than relying on it.
- **D) with** generally indicates accompaniment, not reliance. Saying "I count with your help" suggests that someone is helping in a way that does not emphasize trust or dependence.

In summary, "upon" in this context highlights the speaker's expectation and trust in the other person's assistance, making it the correct choice in the phrase "I count upon your help."