Paul was a gifted and focused man, with numerous 'strings to his bow', but he made his life's priority 'spreading the good news of Jesus Christ' to the gentiles. That was his 'why?' in life. He stated this 'why' at the very beginning of his letter to the Romans, and now he draws it to an end with the same focus. There are 3 aspects to this part of his letter:
Ministry advice - he expresses his confidence in their ability of spreading the good news
Ministry advance - thanks to the power of the Spirit he is confident the message will grow
Ministry aspiration - he firmly trusts that many who have not heard the gospel will hear it soon.
What is our 'why?' in life? Do we want to spread the news of Christ? Let's take Paul's words of confidence, of assurance of the power of the Spirit, and trust that new people will hear the good news, for ourselves.