Numbers not creating a line graph
It is a bit hard to say from the picture you have shared but you may not be doing anything wrong at all. Here is a chart I created with similar data with yours. 



I just selected the numbers to be charted (but did not select either the header row or the header column) and then clicked on Chart in Numbers toolbar at the top and selected the icon representing the 2D line chart.

Numbers behave in a weird fashion sometimes in creating charts in my experience. This happens to me occasionally even when I am creating simple charts. When this happens, I create a new file, copy the data only to the new file and create a new chart usually using the same steps. Those steps that have failed in my first trial usually work in the second trial!