1. Find the starting INITIAL BEFORE VALUE and the LATEST AFTER VALUE

As Pete says, it is difficult to know what you are asking but here's my best guess.

You know that the "Before Value" of a row is taken from the "After Value" of the preceding row.

Row[N].Before_Value = Row[N-1].After_Value

A "group" of rows or an "input set" is terminated when this "rule" is not respected.

You can therefore traverse the rows of the table testing for this condition and when it is not true then you have found the end of one input set (the LATEST AFTER VALUE of the current input set) and the start of the next one (the INITIAL BEFORE VALUE of the next input set).

Doing that would give you the output that you have put into the question and the "What I have tried" section.

As an aside, there are 5 input sets and not 4 as you state in your question, this is shown in the output that you have provided.

As for what code would do that for you then you need to show what code you have tried (so people can help you improve it / fix it) or as an absolute minimum the language that you are supposed to be using.

You are missing so much context here that it is impossible for us to come up with a reasoned view of what you are trying to solve. In your example, I have to assume that the space between sections is indicating that these are the groups you need to find the first value and last value from but, there's no indication how this would work in a database context.

To be honest, this sounds like a homework question and you have missed out parts of what has been asked. As we can't see your screen, we have no idea what you need to do to complete this. Also, you haven't shown what you have tried - you say this is a SQL question but you haven't actually put any SQL in there.