The most appropriate option to fill in the blank is:

☀ across

Explanation:

The sentence "He ran across the field to catch the ball" indicates that the person ran from one side of the field to the other in order to catch the ball. "Across" is the correct choice here because it accurately conveys the idea of moving from one side to the opposite side of the field.

The other options have slightly different meanings:

• "Over" might imply jumping over something or moving on top of something, but it doesn't convey the idea of moving from one side to the other side of the field.
• "Through" implies moving within something or passing through a space, but it doesn't necessarily indicate moving from one side of the field to the other.
• "Besides" means next to or alongside, which doesn't fit the context of running across the field.