For most of the time throughout the picnic, the boys . . . . . . . . football while the girls . . . . . . . . flowers.

The correct answer is: D. were playing/were picking

The sentence is in the past tense, so we need to use verbs in the past tense. The boys were playing football, and the girls were picking flowers.

• Will play/have been picking is incorrect because it is in the future tense. The sentence is about what happened in the past, not what will happen in the future.
• Are playing/have been picking is incorrect because it is
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  in the present tense. The sentence
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  is about what happened in the past, not what is happening now.
• Have played/are picking is incorrect because it is a combination of the past tense and the present tense. The sentence is about what happened in the past, not what is happening now.
• Had been playing/have picked is incorrect because it is a combination of the past perfect tense and the present perfect tense. The sentence is about what happened in the past, not what has happened up to now.

Therefore, the correct answer is D. were playing/were picking.