This segment addresses thanks in Acts. We've already looked at one passage in Acts where Paul thanks God for the food that he's about to eat. There are two other examples of thanks in Acts as well.
The first example is Tertullus' thanks of Felix - an attempt to flatter Felix and win him over so that Paul could be attacked. The second example is Paul giving thanks to God for the brethren who joined them on the journey to Rome.
The first example illustrates for us the fact that kings liked to be thanks for doing a good job governing. We are not to try to flatter God, but we ought to glorify and give him praise for his excellent governance of this world. While we may not always fully appreciate it, God governs the world well.
The second example further reminds us to give thanks to God for his providences, even those involving the "free" acts of men. Notice that Paul does not simply thank the brethren for joining him, but thanks God. This kind of thanks to God makes sense if we adopt a Calvinistic viewpoint of the free will of men, but not if we adopt a Libertarian view of freedom. If man is under God's providence, it makes sense to thank God for the actions of men. If man is autonomous, thanking God for men's actions makes no more sense than thanking your fellow man for a third man's actions.
And after five days Ananias the high priest descended with the elders, and with a certain orator named Tertullus, who informed the governor against Paul. And when he was called forth, Tertullus began to accuse him, saying,
Seeing that by thee we enjoy great quietness, and that very worthy deeds are done unto this nation by thy providence, we accept it always, and in all places, most noble Felix, with all thankfulness. Notwithstanding, that I be not further tedious unto thee, I pray thee that thou wouldest hear us of thy clemency a few words. For we have found this man a pestilent fellow, and a mover of sedition among all the Jews throughout the world, and a ringleader of the sect of the Nazarenes: who also hath gone about to profane the temple: whom we took, and would have judged according to our law. But the chief captain Lysias came upon us, and with great violence took him away out of our hands, commanding his accusers to come unto thee: by examining of whom thyself mayest take knowledge of all these things, whereof we accuse him.
And the Jews also assented, saying that these things were so.
And after three months we departed in a ship of Alexandria, which had wintered in the isle, whose sign was Castor and Pollux. And landing at Syracuse, we tarried there three days. And from thence we fetched a compass, and came to Rhegium: and after one day the south wind blew, and we came the next day to Puteoli: where we found brethren, and were desired to tarry with them seven days: and so we went toward Rome.
And from thence, when the brethren heard of us, they came to meet us as far as Appii forum, and The three taverns: whom when Paul saw, he thanked God, and took courage. And when we came to Rome, the centurion delivered the prisoners to the captain of the guard: but Paul was suffered to dwell by himself with a soldier that kept him.