Hardly a day passes by … him thinking of her.

Analyze the question: The sentence is "Hardly a day passes by _ him thinking of her." We need the word that links the two parts so the meaning makes sense.

Concept: "Hardly a day passes" is a near-negative idea. It means almost every day, he thinks of her. A common English structure is "not a day passes without + -ing". "Hardly a day passes without him thinking of her" follows the same pattern, so the preposition without is needed.

Step-by-step check of the options:

• A. that: "Hardly a day passes by that him thinking of her" is ungrammatical. "That" would need a subject pronoun (e.g., "that he thinks"), not "him thinking".
• B. without: "Hardly a day passes by without him thinking of her" is grammatical and means "he thinks of her almost every day." ✔
• C. while: "while him thinking" is ungrammatical and does not fit the meaning.
• D. when: "Hardly a day passes by when him thinking of her" is ungrammatical. "When" would need "he thinks".

Answer: B. without

Exam tip: Whenever you see "hardly / scarcely / not a day / never a day ... " followed by a verb in -ing form, think of "without." Remember the pattern: "Not a day passes without ___ing." It means the action happens almost every day.