Well, I know you don't want to hear this, but your data is in the wrong arrangement. Unfortunately, we receive data with little control over its arrangement, or someone is too invested in the pretty table they painstakingly formatted.
The best arrangement would be a four-column array, with one column each for Year, Month, Product, and whatever the dollar value represents (presumably Sales). Then you could build a pivot table, filter on year, and plot the three lines. (You could also make a second pivot table with the arrangement shown in your first post.)
Fortunately, your data isn't too complicated and is regular enough, that a few simple formulas can give you a chart data range that you can use. It looks like the following. The numbers are not the same, because I wasn't about to type all those numbers from a screenshot.
I put the months in the left column of the staging area (N3:N14) and the products in the first row (O2:Q2). The year goes in the top left corner (N2). To make it easy to choose a year (rather than having to type it in manually) I set up a Data Validation dropdown in cell N2, allowing a list whose source is $C$2:$L$2, the years from your original table.
The magic formula in cell O3 is:
Excel Formula:
=INDEX($C$3:$L$38,MATCH($N3,$A$3:$A$38,0)+MATCH(O$2,$B$3:$B$5,0)-1,MATCH($N$2,$C$2:$L$2,0))
I made a dynamic chart title in cell N16 using this formula:
Excel Formula:
=N2&" Product Sales by Month"
Then I made a chart using the range N2:Q14. To get that title into the chart, I selected the chart title, typed = into the formula bar, then clicked on cell N16 and pressed Enter.