The given information in sentence 1 is “the M6”. The reader knows about the M6 (it’s a motorway) but does not know its destination and so needs to be told. The fact that it goes from Birmingham to Carlisle is the new information.
In sentence 2, the given information is “the motorway from Birmingham to Carlisle”. The reader knows there is a motorway from Birmingham to Carlisle but does not know what it is called. The fact that it is called the M6 is the new information for the reader.
In English, the given information usually comes at the beginning of the sentence and the new information at the end. The decision about which part of the sentence to make the given information and which part to make the new information is the choice of the writer and depends on the organisation of ideas in the whole paragraph (and in previous paragraphs). In other words, the writer organises information based on what the reader knows.
Let’s look at two more examples.