Answer:
Although you didn't say which is the underlined verb, I assume it is prepare, since it is the only one in infinitive that would need an adjustment. So, The correct answer would be: <em>By the time you have arrived, we will be preparing to go home.</em>
Explanation:
The <em>Future Progressive Tense</em> is the one that indicates a continuing action, something that will be happening or going on at a specific point in the future. It is formed with the modal "<em>will</em>" plus "<em>be</em>", plus the present participle of the verb (with an -ing ending). In this case, the specific point in the future would be By the time you have arrived, and the modal <em>will</em>, plus <em>be</em>, plus <em>preparing</em> (the present participle of prepare).
