I'm trying to make a chart like this:
And my data is organized like this:
I'm just not sure how my chart needs to be organized in terms of series to achieve this.
This is a pivot chart as opposed to a regular chart in Excel. Pivot charts are closely related to pivot tables and you can find an introduction to them both here.
Your data layout is not optimised for pivoting but you can probably generate the memory chart as shown with no changes.