Answer:
The great Roman Empire was so powerful that it conquered a large part of Europe, as well as parts of Africa and Asia.
The Puritans had to face many obstacles and mischiefs on their way to the New World.
(The compound objects are bold, as I cannot underline them.)
If a direct object is the recipient of action of the verb (what the verb does to something/someone), a compound direct object is composed of two or more such recipients.
