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Looks like [Statement Month Year] is a date field, so you should be able to just drag it to the Marks shelf and drop it on the Colors box, and it will by default add it as YEAR([Statement Month Year]).
Having that on the Marks shelf for color will automatically cause a line chart to separate into separate lines per year.
Then put MONTH([Statement Month Year]) on your Columns shelf to complete the structure.
Screenshot from Superstore attached to illustrate.
EDIT: What Shawn said!
I am on Tableau 10.1.3 - Don't know if you can open the attached - but see below
Put your date on the columns shelf and set to MONTHS
Your measure will go to rows
and Years go to the color tile on the marks card
Does this work for you?
double line chart.twbx 1.2 MB