Explanation:

- It was impossible to guess what he was doing.

- Option 1: "to"

- Functions as the infinitive marker often used to express capability or possibility.

- Correct usage here because it's common in English to say "impossible to guess."

- It was impossible at guess what he was doing.

- Option 2: "at"

- Typically indicates location or time.

- Incorrect here as it doesn't logically fit the context.

- It was impossible on guess what he was doing.

- Option 3: "on"

- Used to denote surfaces or dates.

- Incorrect because it doesn’t align with the structure of guessing.

- It was impossible of guess what he was doing.

- Option 4: "of"

- Often implies belonging or association.

- Incorrect here as it doesn’t fit the construction.

Answer: Option 1 - "to"

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