Okay, even though we don't have a map, our knowledge of history will help us. :)
So, we know that ancient Egypt's late period occurred between 664 and 332 BCE. We also know that the Persian empire came to be in 550 BCE, when it was founded by Cyrus the Great. This means that both of these empires existed roughly at the same time. Thus, the correct answer is this:
According to the map below, the Persian empire was in existence at the same time as ancient Egypt late period, which lasted until 332 BCE, and the Persian empire until 330 BCE.
