We know from the clause "he had no time to eat" that the person in question was so busy or occupied that they did not have any open time in their schedule dedicated to eating. This implies that their level of busyness was so great it prevented them from a basic activity of daily living.

Of the answers provided, only one option conveys this exact sense of meaning - "so busy that." Saying someone was "very busy" or "busy" alone does not directly connect their busyness to the lack of time to eat. "Too busy" and "very busy that" come close but do not have quite the right emphasis.

"So busy that" most accurately and completely fills in the missing information to form a sentence that reads clearly and logically. It directly attributes the subject's inability to eat due to a specifically high degree of busyness.