I assume that what this question is really asking is something like “how do all of these things go together.” This is because these four things cannot really have anything in common. Andrew Johnson was one person, the Radical Republicans were many people, impeachment is a process, and Congressional Reconstruction was an event. These things do not have anything in common. However, they do go together very well.
Here is a sentence that puts them all together. “The Radical Republicans became angry at Andrew Johnson’s policies so they impeached him and initiated Congressional Reconstruction.” Let us explain this sentence.
Andrew Johnson was the president of the US after Abraham Lincoln was assassinated. He proposed a very lenient Reconstruction program, much as Lincoln had. However, the Radical Republicans (who controlled Congress) were very angry at the South and did not want to be lenient. They felt that the South had to be punished for causing the Civil War. They disagreed strongly with Johnson and came into conflict with him. Eventually, the conflict became so bad that they impeached him, though he was not convicted and remained in office. While they were not able to remove him from office, they did defeat his Reconstruction program and implemented Congressional Reconstruction, which was much more punitive than Johnson’s program had been.
On February 24, 1868, for the first time in history, the US House of Representatives impeached a sitting president, Andrew Johnson. After Lincoln was assassinated, Vice President Johnson assumed office. He was a union man, but his roots were in the south. "This is a country for white men," he had stated. So he failed to win favor with radical Republicans. Johnson believed the Reconstruction Acts, laws that provided suffrage (the right to vote) to freed slaves (men) and prevented former southern rebels from gaining control of state governments, were unconstitutional. He repeatedly blocked their enforcement. Johnson's open defiance of Congress led to his impeachment.