2002 Mazda protege. Shifter cable broke from the selector lever (i believe those are the correct terms). Anyone have an idea of how I might fix this?
From the photo angle it looks like you need a new shifter cable and a new “manual lever” for the transmission.
Those usually come as a unit so you will be replacing from the clutch pedal back most likely .Probably a Mazda only part unless you get real lucky and find a used manual Mazda in a junkyard .
It’s not a stick shift car
You can clearly see the automatic transmission pan in the picture 
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Well yeah, plus you can see that the lever only slides in one direction, which would be further evidence that this is an Automatic.