"You can verify", he was able to say to Felix. Felix could easily verify the truth of Paul's claims that in Jerusalem he had not been disputing or stirring up a crowd, or in any other way causing trouble. He had, in fact, been humbly performing certain actions so as to avoid offense to the Jews (Acts 21:20-26). Because of Paul's submission to the elders and his desire to not give unnecessary offense, his character and actions were easily vindicated. This goes along with many instructions to us in God's word to "live above reproach" for the sake of the gospel (Titus 2:1-12).
"Neither can they prove to you what they now bring up against me", Paul was also able to say to Felix. The Jews had traveled to Caesarea to bring charges against Paul with nothing in their arsenal but false flattery for Felix (Acts 24:1-9). They had no proof for their accusations ("he is a plague, he stirs up riots, he tried to profane the temple") because there was no proof; Paul was innocent of these things. Yes, there were riots around Paul, but he hadn't caused them. The fury of the unbelieving Jews against the truth of the gospel was the reason for that rioting. Truth often brings division, but truth is not at fault for it. Rather, the unbelief of the hearers brings it about.
God made sure that these charges against Paul wouldn't stick. God wanted Paul to be found "guilty" of only one charge: preaching the gospel of the Lord Jesus Christ. It had been the Lord's plan and predetermined purpose to bring Paul to Rome in order to testify about Him (Acts 23:11). The means He had used to that end were tumultuous: an angry mob, the beating of Paul, and a narrow escape from a plot against his life. All these things He had ordained that his servant Paul might stand before governors and kings and testify to them about Christ.
I see from these accounts how we should also aim to live, trusting God's providential ordering of our steps, so that if the time comes we can truthfully say, for the gospel's sake, "You can verify" and "neither can they prove".
"Keep your conduct among the Gentiles honorable, so that when they speak against you as evildoers, they may see your good deeds and glorify God on the day of visitation" (1 Peter 2:12).
"This is evidence of the righteous judgment of God, that you may be considered worthy of the kingdom of God, for which you are also suffering—since indeed God considers it just to repay with affliction those who afflict you, and to grant relief to you who are afflicted as well as to us, when the Lord Jesus is revealed from heaven with his mighty angels in flaming fire, inflicting vengeance on those who do not know God and on those who do not obey the gospel of our Lord Jesus.
"They will suffer the punishment of eternal destruction, away from the presence of the Lord and from the glory of his might, when he comes on that day to be glorified in his saints, and to be marveled at among all who have believed, because our testimony to you was believed.
"To this end we always pray for you, that our God may make you worthy of his calling and may fulfill every resolve for good and every work of faith by his power, so that the name of our Lord Jesus may be glorified in you, and you in him, according to the grace of our God and the Lord Jesus Christ" (2 Thessalonians 1:5-12).