To answer this question, we need to understand the correct usage of verbs in this context.
Option A) "do" - This option is correct because it uses the base form of the verb "do" to indicate that the children are actively performing the action of their homework.
Option B) "to do" - This option is incorrect because it uses the infinitive form of the verb "to do" without a main verb to support it. In this sentence, we need a main verb to convey the action of doing homework.
Option C) "studied" - This option is incorrect because it uses the past tense form of the verb "study", which is not suitable for the present tense context of the sentence.
Option D) "to study" - This option is incorrect for the same reason as option B. It uses the infinitive form of the verb "to study" without a main verb.
The correct answer is option A) "do". This option is correct because it uses the base form of the verb "do" to indicate that the children are actively performing the action of their homework.